Week 10 Tutorial Exercises
Readings
Read Chapter 9 thoroughly.
Make sure that you know the meanings of the Key Terms at the chapter end.
Review Questions (these may or may not be discussed in tutorial classes)
What is functional form misspecification? What is its major consequence in regression analysis?
As the word “misspecification” suggests, it is a mis
‐
specified model with a wrong functional form
for explanatory variables. For example, a log wage model that does not include
age
2
is mis
‐
specified if the partial effect of age on log wage is upside
‐
down
‐
U shaped. In linear regression
models, the functional form misspecification can be viewed as the omission of a nonlinear
function of the explanatory variables. Hence the consequences of omitting important variables
apply and the major one is estimation bias.
How would you test for functional form misspecification?
The RESET may be used to test for functional form misspecification, more specifically, for
neglected nonlinearities (nonlinear function of regressors). The RESET is based on the F
‐
test for
the joint significance of the squared and cubed predicted value (y
‐
hat) in a “expanded” model
that includes all the original regressors as well as the squared and cubed y
‐
hat, where the latter
represent possible nonlinear functions of the regressors.
What are nested models? And, nonnested models?
Two models are nested if one is a restricted version of the other (by restricting the values of
parameters). Two models are nonnested if neither nests the other.
What is the purpose of testing one model against another?
The purpose of testing one model against another is to select a “best” or “preferred” model for
statistical inference and prediction.
How would you test for two nonnested models?
There are two strategies. The first is to test exclusion restrictions in an expanded model that
nest both candidate models and decide which model can be “excluded”. The second is to test
the significance of the predicted value of one model in the other model (known as Davidson
‐
MacKinnon test).
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 One '11
 yang
 Yi, OLS, lnchprg, functional form misspecification, Bixi

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