A Paasche index of prices is sometimes used by economists as a way of estimating inflation. It works by comparing the price of a current representative basket of goods with its price in previous years.
By 'representative' I mean that the basket reflects what consumers are spending their money on in the current period. The problem with the Paasche Index is that today's representative basket may have little relevance for previous years, and especially so the more distant those years are.
Consider, for example, that today's representative basket will probably include items like smart phones, electric cars, Netflix subscriptions and all sorts of other products that didn't exist until recently. This presents a problem for anything but short-term comparisons in the changing cost of living.
The problems with the Paasche Index do not stop with the introduction of previously unavailable goods and services. Consumer preferences change as the relative prices of existing goods change, meaning that a representative basket today will be different to previous periods if the relative price of specific goods has changed. I will give an example of this below, but the implication is that the Paasche Index will have a downward bias that underestimates inflation and the changing cost of living.
The Paasche Index Formula can be expressed as the price of the current representative basket of goods & services divided by the price of the same basket in a previous year.
Current representative basket / same basket in a previous year x 100
The previous year may be last year or several years ago, and it is regarded as a base year with a price equal to 100.
Suppose that 3 representative baskets are purchased in the current year for a total cost of $420. The cost in the base year would be $300 since each basket costs $100 in that base year. The Paasche Index score is then 420/300 x 100 = 140
In other words, the cost of living in the current year has risen by 40% since the base year since 140 is 40% more than 100.
As mentioned above the Paasche Index comes with a downward bias that underestimates the true rising cost of living over time because today's basket of goods may not be representative of what consumers were preferring to purchase in the base year.
This is a problem because an accurate cost of living index needs to estimate the cost of attaining a given level of 'utility' from the things that they purchase. If some items that are currently being consumed were relatively more expensive in the base year then consumers would have preferred to substitute cheaper alternatives to obtain the same total utility.
For example, imagine that the basket contains only two items, cheese and biscuits. Assume that, if the price of both items was $1 each in the base year, the preferred consumption would be 50 servings of cheese and 50 servings of biscuits for a total cost of $100.
Now, in the current year the relative cost of cheese has risen. Cheese now costs $2 per serving, but biscuits are unchanged at $1 per serving. Consumers will maximize their utility in the current year with a preferred consumption of, for example, 40 servings of cheese and 60 servings of biscuits for a total cost of $140. Since, in the base year, 40 servings of cheese and and 60 servings of biscuits would have cost $100, the Paasche Index estimates that the cost of living has risen by 40% since the base year.
However, we know that consumers in the base year would have preferred 50 servings of both cheese and biscuits. This means that the utility from 40 servings of cheese and 60 servings of biscuits is somewhat less. Perhaps utility would be equal if 40 servings of cheese were consumed with 70 servings of biscuits in the current year. In that case the true cost of living index would currently be (40x2) + (70x1) = 150
Clearly, 150 is higher than 140, so the Paasche Index estimate of a 40% increase in the cost of living understates the true cost of living i.e., 50%. This is the Paasche Index downward bias.
While the Paasche Index focuses on the cost of the current preferred basket of goods & services, the Laspeyres Index uses a basket that is fixed in the base year, and then calculates the cost of buying that fixed basket in later years. It has the opposite problem that the Paasche Index suffers in that it tends to overestimate inflation and the rising cost of living. For more details, see my article about:
The Fisher Index attempts to overcome the upward and downward biases of the Laspeyres and Paasche Indexes by taking a geometric average of the two. However, it has its own problems and it certainly is not a perfect cost of living index. For more details, see my article at: