Eric, thank you for your interesting example (below). In the case you
mention people's real income has clearly gone up, unlike that which has
confronted most of us lately. How do we know this? The quantities, 10 of
each good, which were purchased in Year 1 could have been purchased for
$300*10 + $150*10 = $4500
in year 2, just the 125% increase implied by an increase of 225% in the
fixed weight index. In fact people had $5100 to spend, and hence they were
better off in Year 2. In fact, people could afford 11.33 units of each good
in Year 2. In fact they purchased 14 units of good A and 6 units of good B
in Year 2. Presumably they are better off with their actual purchases than
by continuing with their previous pattern of purchasing equal quantities of
each. The magnitude of the substitution effect is the amount by which they
are better off with the new commodity bundle rather than the old. Since the
old, the proportionate increase, is always available, the substitution
effect can never be negative.
Dave Richardson
----------
From: pen-l
Subject: [PEN-L:3957] RE: the CPI
Date: Thursday, April 25, 1996 11:48AM
Forgive possible double posting, but my message
from yesterday never appeared on pen-l. In any case, I've
revised it to make it more clear.
D Richardson wrote:
> . . . the substitution bias is always positive. The answer is from
> the micro theory textbook: as relative prices change people
> substitute toward the now less expensive goods and away from
> the more expensive . . .
I disagree. The sign of the substitution bias is an empirical
matter and not a "theoretical" matter. The sign of the
substitution effect can be negative or positive.
Example:
Assume two goods (A and B) experience price increases
between year 1 and 2. Assume good B increases in price
faster than good A. Therefore, people shift to buying more
of good A in year 2 compared to year 1.
year 1 | year 2
good P rel P Q z P relP Q
A 150 3 10 z 300 2 14
B 50 1 10 z 150 1 6
CPI: year 1 150x10+50x10 = 2000
year 2 300x10+150x10 = 4500 =225% increase
using fixed weights (from year 1)
But, expenditures in the two years are
year 1 150x10+50x10 = 2000
year 2 300x14+150x6 = 5100 = 255% increase
using actual buying patterns
That is, in this case the CPI UNDERSTATES the rate
of inflation experienced by consumers: CPI
indicates 225% inflation rate while expenditures by
consumers go up by 255%.
Why? In this case the good that has its relative price
falling between years 1 and 2 is the HIGHER priced
good. A shift to a good whose relative prices has fallen
need not be a shift to a lower priced good.
The substitution bias only has a systematic downward
impact on the CPI if goods that are LOW priced in the
base year tend have their relative price FALL in later years.
But there is no theoretical reason for this to occur. In
fact, there are likely good reasons to suppose that goods
that have their relative prices fall were HIGH priced goods
to begin with.
Conclusion: "theory" does not imply that the CPI necessarily
overstates "true" inflation rates (based on the substitution effect).
Eric
..
Eric Nilsson
Department of Economics
California State University
San Bernardino, CA 92407
[EMAIL PROTECTED]
