Measurement Units & Dummy Variables in Econometrics: Hypothesis Tests, Interaction Effects, Slides of Econometrics and Mathematical Economics

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Econometrics

Chapter 9 -- Functional Form II :

Further topics

Units of measurement

• Suppose the original model is given by:

 If the variables are rescaled (due to a

change in units of measurement), the

transformed variables may be

expressed as:

Hypothesis tests and changes in units

of measurement

• t – and F -statistics are unaffected by changes

in units of measurement

Significant digits

• Report as many digits in the results as there

are significant digits in the raw data.

Interaction effects

• Interaction effects are used when the marginal

effect of a variable is affected by the level of

another variable.

• Example: IQ and schooling may have an

interaction effect in an earnings equation

Dummy variable

• Dummy variables are used to represent qualitative

variables such as:

• Gender
• Race
• Geographical location
• Educational attainment
• Policy changes
• Dummy variable, D i = 1 if characteristic is present for

observation i and D i = 0 if the characteristic is not

present

Difference in intercept

• To test for gender difference in intercept:
  • H (^) o: β 2 = 0

Example: Earnings equation

Example: Earnings equation

Dummy variables in practice

• It is common practice to have sets of dummy

variables in a regression equation to capture the

effect of qualitative variables.

• Examples:
  • Race (black, Hispanic, Asian, native American
  • Geographical location (rural/urban or NE, S, W)
  • Alternative levels of educational attainment

Example: Earnings and educational

attainment

Example: Earnings and educational

attainment (cont.)

Chow Test: Method I

1. Define a dummy variable that equals 1 in one subgroup and 0 in the other.
2. Estimate an unrestricted version of the model that include a dummy variable and interaction terms between the dummy variable and each slope variable (this allows all parameters to vary between the two subgroups)
3. Estimate a restricted model without the dummy variable and interaction terms.
4. Perform a Wald test to test for the joint significance of the coefficients on the dummy variable and all interaction terms involving the dummy variable. d.f. = (k+1),N- 2(k+1)
5. Reject the null hypothesis if the F - statistic exceeds the critical value at the pre-selected significance level. Docsity.com

Chow test: Method II

1. Sort the sample into the appropriate two

subgroups.

2. Estimate the equation separately in each

subsample and save the ESS for each equation. The

unrestricted ESS equals the sum of the ESS in these

two equations.

3. Estimate the parameters using the entire sample to

compute the restricted ESS.

4. Perform a Wald test.