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

Engel expenditure
models, named after the
German statistician Ernst Engel, 1821–1896. (See Exercise 6.10.) Engel postulated that
“the total expenditure that is devoted to food tends to increase in arithmetic progression as
total expenditure increases in geometric progression.”
18 
17
Again, using differential calculus, we have
dY
d X
=
β
2
1
X
Therefore,
β
2
=
dY
d X
X
=
(6
.
6
.
12)
18
See Chandan Mukherjee, Howard White, and Marc Wuyts, 
Econometrics and Data Analysis for Devel-
oping Countries,
Routledge, London, 1998, p. 158. This quote is attributed to H. Working, “Statistical
Laws of Family Expenditure,” 
Journal of the American Statistical Association, 
vol. 38, 1943, pp. 43–56.
As an illustration of the lin–log model, let us revisit our example on food expenditure in
India, Example 3.2. There we fitted a linear-in-variables model as a first approximation.
But if we plot the data we obtain the plot in Figure 6.5. As this figure suggests, food
expenditure increases more slowly as total expenditure increases, perhaps giving credence
to Engel’s law. The results of fitting the lin–log model to the data are as follows:
FoodExp
i
= −
1283.912
+
257.2700 ln TotalExp
i
t
=
(
−
4.3848)*
(5.6625)*
r
2
=
0.3769
(6.6.14)
Note:
* denotes an extremely small 
p value
.
(
Continued
)
EXAMPLE 6.5
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