INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN 83
ii. The indirect methods. First,
you may try to reduce . The disturbance term is the joint effect of all the variables influencing
Y that you have not included explicitly in the regression equation. If you can think of an important variable that you have omitted, and is therefore contributing to
u, you will reduce the population variance of the disturbance term if you add it to the regression equation. Second, consider
n, the number of observations. If you are working with cross-section data (individuals,
households, enterprises, etc) and you are undertaking a survey, you could increase the size of the sample by negotiating a bigger budget. Alternatively, you could make a fixed budget go further by using a technique known as clustering. A further way of dealing with the problem of multicollinearity
is to use minor information, if available, concerning the coefficient of one of the variables.
…[2.70] For example, suppose that
Y in equation is the aggregate demand fora category
of consumer expenditure,
X is aggregate disposable personal income, and
P is a price index for the category. To fit a model of this type, you would use time series data. If
X and
P possess strong time trends and are therefore highly correlated, which is often the case
with time series variables, multicollinearity is likely to be a problem. Suppose, however, that you also have cross-section data on
Y and
X derived from a separate household survey. These variables will be denoted
Y' and
X' to indicate that the data are household data, not aggregate data. Assuming that all the households in the survey were paying roughly the
same price for the commodity, one would fit the simple regression
̂
…[2.71] Now substitute
for
in the time series model
…[2.72]
Subtract from both sides,
