Chapter
7: TOPICS IN REGRESSION ANALYSIS
1. Proxy variables: least
squares estimators are unbiased only when all relevant independent variables
are specified. Sometimes difficulty in
measuring influences requires the use of proxy variables. Examples include:
a.
Use of measures of consumer confidence to measure expectations.
b.
Use of unemployment rate to measure expected income.
Proxy
variables are more useful in forecasting with time series data since they may
reflect the change in the theoretical variable being measured. However, they may be misleading when used as
an explanatory model for simulation.
2. Dummy
variables: used to represent the
influence of qualitative variables (gender, age, market segments, special
events in time series (war years), and seasonal variation. It can also be used to test for structural
stability in intercept and slopes. A
dummy variable is indicated when a consistent set of outliers exist that may be
due to some irregular influence.
3. Selecting
the best forecasting model: The
best model includes all of the important explanatory variables and does not
include variables that are not important explanatory variables. Hence, the t-values of all included
variables indicate that a significant causal effect exists for that independent
variable. Two techniques of deciding on
the best model when several possible independent variables exists are:
a.
Estimate all the possible regression equations and select the one with
the highest adjusted R-squared (lowest standard error of the regression) with
all of the t-values significant.
b.
Use stepwise regression and allow the computer to select in succession
the independent variables for which the additional explained variance is
significant.
4. Lagged
variables. There are two types of
lagged relationships that may be introduced into the equation.
a.
Simple lagged relationships use only one time period for the independent
variable with the lag in that time period based upon the highest correlation
(best fit) with the dependent variable.
b.
Distributed lags use more than one time period for the independent
variable due to delayed responses that are spread out over a large number of
periods. The weights applied to each
lagged value of the independent variable may be determined by the regression
coefficients. (See example 7-11 on page
325). An example is the forecast of
changes in quarterly consumption spending based upon past quarterly changes in
disposable personal income as well as the current rate of interest. (See example 7-12) The weighted average of past changes in income represents an
estimate of expected income.
In the material to follow we will
see that autoregressive methods used combinations of present and past values of
an observation in order to forecast its future value. Hence, this adaptive expectations model is really a combination
of autoregressive techniques with regression (causal) technique.