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

FIGURE 6.4 
guj75772_ch06.qxd 07/08/2008 07:00 PM Page 163

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Part One
Single-Equation Regression Models
Instantaneous versus Compound Rate of Growth
The coefficient of the trend variable in the growth model (6.6.6),
β
2
, gives the
instantaneous
(at a point in time) rate of growth and not the
compound
(over a period of time)
rate of growth. But the latter can be easily found from Eq. (6.6.4) by taking the antilog of
the estimated
β
2
and subtracting 1 from it and multiplying the difference by 100. Thus, for
our illustrative example, the estimated slope coefficient is 0.00705. Therefore,
[antilog(0.00705)
−
1]
=
0.00708 or 0.708 percent. Thus, in the illustrative example, the
compound rate of growth
on expenditure on services was about 0.708 percent per quarter,
which is slightly higher than the instantaneous growth rate of 0.705 percent. This is of course
due to the compounding effect.
Linear Trend Model
Instead of estimating model (6.6.6), researchers sometimes estimate the following model:
Y
t
=
β
1
+
β
2
t
+
u
t
(6.6.9)
That is, instead of regressing the log of 
Y
on time, they regress 
Y
on time, where 
Y
is the
regressand under consideration. Such a model is called a 
linear trend model
and the
time variable 
t
is known as the 
trend variable. 
If the slope coefficient in Equation 6.6.9 is
positive, there is an 
upward trend
in 
Y
, whereas if it is negative, there is a