Download Model Identification Summarizing Empirical Estimation EconS 451: Lecture #9

EconS 451: Lecture #9
Summarizing Empirical Estimation
• Transforming Variables to Improve Model
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?
• Using Dummy / Indicator Variables
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• Issues related to Model Identification.
Price
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• Why Deflate Data?
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• What time series do we use?
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• How to identify:
• Heteroskedasticity
• Multicollinearity
• Autoregression
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Quantity
Model Identification
If the economy were perfectly static……it would be
impossible to estimate either demand or supply.
Model Identification
Price
S1
but supply and demand functions shift with the passage
of time, thus allowing one or both to be estimated.
S2
S3
Supply
Price
Demand
D3
Quantity
D2
D1
Quantity / Unit Time
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.
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How to Identify….
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.
• Multicollinearity ?
• Visual inspection of Residual Plot.
• Goldfeld-Quandt Test.
H 0 : σ 12 = σ 22
• Set Up and Test Hypothesis
GQ =
• Economic logic.
• Odd signs for estimated coefficients may be first clue.
• Correlation Matrix
H1 : σ 12 ≠ σ 22
∧
2
1
∧
2
2
σ
≈ Fdf1 ,df 2
σ
Multicollinearity
How to Identify….
• Autoregression = error terms are correlated over
Correlation matrix
time
Quantity of
Red Roses
(doz.)
Quantity of Red Roses (doz.)
Price of Red
Roses
(per/doz.)
Quantity of
Orchids
(doz.)
Per Capita
Income
Quantity
of Tulips
(doz.)
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yt = β 0 + β1 xt + ε t
Price of Red Roses (per/doz.)
-0.80
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Quantity of Orchids (doz.)
-0.76
0.97
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Per Capita Income
-0.71
0.48
0.57
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Quantity of Tulips (doz.)
-0.44
0.81
0.98
0.42
Durbin-Watson Test Statistic
T
d =
∧
∑ (e
t =2
t
T
∧
− et −1 )2
∧2
∑e
t =1
• Residuals Plot
• Test Using Durbin-Watson Statistic
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H0 : ρ = 0
H1 : ρ > 0
ε t = ρε t −1 + vt
What to do if you find…….
• Hetereoskedasticity
ƒ Add variable to account for difference
between groups
• Multicollinearity
t
• Drop correlated variable (s) from estimation.
∧
d ≈ 2 (1 − ρ )
• Autoregression
• Add variable to account for the missing
factor over time
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Summary Questions
• What are the five assumptions of the classical linear regression
Summary Questions
• Explain the process involved with identifying the appropriate
functional form to use when estimating a statistical model.
model?
• What rules do we use to identify a model from price and quantity
• 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
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?
estimation…..and how would you do it?
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