Empirical Estimation Review

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Empirical Estimation Review

• EconS 451 Lecture 8

• Describe in general terms what we are attempting
  to solve with empirical estimation.
• Understand why Ordinary Least Squares has been a
  very popular estimation technique.
• Understand the five assumptions of the Classical
  Linear Regression Model.
• Understand how to choose the appropriate
  functional form.
• Understand the applications associated with
  Indicator (Dummy) Variables.
• Estimation Examples.

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What is our goal ?

• Our economic understanding about how certain
  variables interact.leads us to develop a
  functional specification.
• Dependent Variable F (Explanatory Variables)

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How would we define a relationship ?
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We can be more specific!

• Ordinary Least Squares
• Minimizes the sum of the squared errors to
  produce a line that best fits the data.

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How would we define a relationship ?
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Assumptions ofClassical Linear Regression Model

• Assumption 1
• Dependent variable is a linear function of a
  specific set of independent variables, plus a
  disturbance.

• Violations
• Wrong regressors.
• Nonlinearity.
• Changing parameters.

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Assumptions ofClassical Linear Regression Model

• Assumption 2
• Expected value of disturbance term is zero.

• Violations
• Biased intercept.

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Assumptions ofClassical Linear Regression Model

• Assumption 3
• Disturbances (error term) have uniform variances
  and are uncorrelated.

• Violations
• Heteroskedasticity.
• Autocorrelated errors.

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Assumptions ofClassical Linear Regression Model

• Assumption 4
• Observations on independent variables can be
  considered fixed in repeated samples.

• Violation
• Autoregression.

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Assumptions ofClassical Linear Regression Model

• Assumption 5
• No exact linear relationship between independent
  variables.

• Violation
• Multicollinearity.

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Interpreting Results
Regression Statistics Regression Statistics
Multiple R 0.562956
R Square 0.316919
Adjusted R Square 0.298943
Standard Error 37.80161
Observations 40
ANOVA
  df SS MS F Significance F
Regression 1 25193.03 25193.03 17.6303 0.000155854
Residual 38 54300.56 1428.962
Total 39 79493.58      
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Interpreting Results
Variable  Coefficients Standard Error t Stat P-value
Intercept 40.82 22.13 1.842 0.072962
Income 0.128 0.030 4.195 0.000156
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Choosing a Functional Form

• Linear
• Quadratic
• Hyperbola
• Semi-Log
• Double Log
• Log-Inverse

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Choosing a Functional Form

• Use economic theory.
• Plot the independent variable against the
  dependent variable to discern pattern.
• First without any transformation.
• Then make the different transformations that you
  may be interested to see and plot them against
  the dependent variable.

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Using Indicator Variables (Dummies)
Expenditure Income Structural Dummy
52.50 258.30 0
58.32 343.10 0
81.79 425.00 0
119.90 467.50 0
125.80 482.90 0
100.46 487.70 1
121.51 496.50 1
100.08 519.40 1
127.75 543.30 1
104.94 548.70 1

• Capture Structural Change
• Some unusual occurrence that isnt capture
  elsewhere in the other variables

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! Estimation Demo Using Excel !
See Example
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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?