EconS 451: Lecture #9
Summarizing Empirical Estimation
• Transforming Variables to Improve Model
• Using Dummy / Indicator Variables
• Issues related to Model Identification.
• Why Deflate Data?
• What time series do we use?
• How to identify:
• Heteroskedasticity
• Multicollinearity
• Autoregression
Model Identification
Why do we believe that by taking prices and quantities
and estimating a statistical relationship that we’ve
estimated a Demand or Supply Relationship?
35.00
30.00
Price
25.00
20.00
15.00
10.00
5.00
0.00
0.00
20.00
40.00
60.00
Quantity
80.00
100.00
Model Identification
If the economy were perfectly static……it would be
impossible to estimate either demand or supply.
but supply and demand functions shift with the passage
of time, thus allowing one or both to be estimated.
Supply
Price
D3
D2
D1
Quantity / Unit Time
Model Identification
Price
S1
S2
S3
Demand
Quantity
Deflating Price and Income
Two Reasons
• Economic
• Estimate real price and income relationships instead of
nominal.
• Statistical
• Reduce correlation between independent variables.
• Reduce heteroskedasticity.
Time Series
• What time series to include?
• Generally speaking, the greater number of observations the
more confidence in estimated coefficients.
• Time period should reflect the conditions under which you are
attempting to capture.
• What level (yearly, quarterly, monthly, weekly, daily,
hourly, etc.)
• Depends on the type of analysis and availability of data.
How to Identify….
• Heteroskedasticity = non-constant error variance
• Eg cross section of firms, the error term for large firms is
consistently greater than the error of small firms.
• Visual inspection of Residual Plot.
• Goldfeld-Quandt Test.
• Set Up and Test Hypothesis
GQ 

2
1

2
2


H0 :   
2
2
H1 :   
2
2
2
1
2
1
 Fdf1 ,df2
How to Identify….
• Multicollinearity ?
• Economic logic.
• Odd signs for estimated coefficients may be first clue.
• Correlation Matrix
Multicollinearity
Correlation matrix
Quantity of
Red Roses
(doz.)
Price of Red
Roses
(per/doz.)
Quantity of
Orchids
(doz.)
Per Capita
Income
Quantity of Red Roses (doz.)
1.00
Price of Red Roses (per/doz.)
-0.80
1.00
Quantity of Orchids (doz.)
-0.76
0.97
1.00
Per Capita Income
-0.71
0.48
0.57
1.00
Quantity of Tulips (doz.)
-0.44
0.81
0.98
0.42
Quantity
of Tulips
(doz.)
1.00
How to Identify….
• Autoregression = error terms are correlated over
time
• Residuals Plot
• Test Using Durbin-Watson Statistic
yt  0  1 xt   t
 t   t 1  vt
H0 :   0
H1 :   0
Durbin-Watson Test Statistic
T
d 

 (e
t 2
t
T

 et 1 )
2
2
e
t 1
t

d  2 (1   )
What to do if you find…….
• Hetereoskedasticity
 Add variable to account for difference
between groups
• Multicollinearity
• Drop correlated variable (s) from estimation.
• Autoregression
• Add variable to account for the missing
factor over time
Summary Questions
• What are the five assumptions of the classical linear regression
model?
• Describe in words, how Ordinary Least Squares works.
• What is measured by the R-Square term?
• How can you determine if a variable is statistically significant?
• What steps do you take to determine the appropriate functional
form for estimating an equation?
• When would you ever utilize an indicator (dummy) variable in your
estimation…..and how would you do it?
Summary Questions
• Explain the process involved with identifying the appropriate
functional form to use when estimating a statistical model.
• What rules do we use to identify a model from price and quantity
relationships ?
• Why do we deflate data?
• What issues should we consider when conducting time-series
estimations ?
• What techniques can be used to identify Heteroskedasticity and
Multicollinearity?
• If these are present……how do we correct these problems?