The McGraw-Hill Series Economics essentials of economics brue, McConnell, and Flynn Essentials of Economics

Part Two
Relaxing the Assumptions of the Classical Model
(i.e., the 
t
ratios will be small), thereby making it difficult to assess the contribution of one
or more regressors to the explained sum of squares.
As Wetherill notes, in practice two major types of problems arise in applying the classi-
cal linear regression model: (1) those due to assumptions about the specification of the
model and about the disturbances 
u
i
and (2) those due to assumptions about the data.
1
In the
first category are Assumptions 1, 2, 3, 4, 5, 9, and 10. Those in the second category include
Assumptions 6, 7, and 8. In addition, data problems, such as outliers (unusual or untypical
observations) and errors of measurement in the data, also fall into the second category. 
With respect to problems arising from the assumptions about disturbances and model spec-
ifications, three major questions arise: (1) How severe must the departure be from a particular
assumption before it really matters? For example, if 
u
i
are not exactly normally distributed,
what level of departure from this assumption can one accept before the BLUE property of the
OLS estimators is destroyed? (2) How do we find out whether a particular assumption is in fact
violated in a concrete case? Thus, how does one find out if the disturbances are normally
distributed in a given application? We have already discussed the 
Anderson–Darling
A
2
statistic
and 
Jarque–Bera
tests of normality. (3) What remedial measures can we take if
one or more of the assumptions are false? For example, if the assumption of homoscedasticity
is found to be false in an application, what do we do then?
With regard to problems attributable to assumptions about the data, we also face similar
questions. (1) How serious is a particular problem? For example, is multicollinearity so
severe that it makes estimation and inference very difficult? (2) How do we find out the
severity of the data problem? For example, how do we decide whether the inclusion or
exclusion of an observation or observations that may represent outliers will make a
tremendous difference in the analysis? (3) Can some of the data problems be easily reme-
died? For example, can one have access to the original data to find out the sources of errors
of measurement in the data?
Unfortunately, satisfactory answers cannot be given to all these questions. In the rest of
Part 2 we will look at some of the assumptions more critically, but not all will receive full
scrutiny. In particular, we will not discuss in depth the following: Assumptions 2, 3, and 10.
The reasons are as follows:
Assumption 2: Fixed versus Stochastic Regressors
Remember that our regression analysis is based on the assumption that the regressors are
nonstochastic and assume fixed values in repeated sampling. There is a good reason for this
strategy. Unlike scientists in the physical sciences, as noted in Chapter 1, economists gener-
ally have no control over the data they use. More often than not, economists depend on sec-
ondary data, that is, data collected by someone else, such as the government and private
organizations. Therefore, the practical strategy to follow is to assume that for the problem at
hand the values of the explanatory variables are given even though the variables themselves
may be intrinsically stochastic or random. Hence, the results of the regression analysis are
conditional upon these given values.
But suppose that we cannot regard the 
X
’s as truly nonstochastic or fixed. This is the
case of