To illustrate how these three indexes yield different measures of inflation, we pro-vide two examples: one during an era of high inflation, and one during an era of little or no inflation. The three items in this case study represent (a) a commodity whose quality does not change very much and whose price changes about the same amount as the overall rate of inflation, (b) a high-tech item whose price falls sharply relative to overall inflation, and (c) a service whose price rises faster than overall inflation.
In the first case, when inflation is rising rapidly, all three measures give approx-imately the same answer. In the second case, when inflation is not rising very much, the estimates diverge significantly. Among other things, that indicates how unrealistic it is to talk about ‘‘zero inflation’’ when the definition depends so much on how inflation is measured. By comparison, when prices are rising 10% a year, the method of measuring inflation is not as important.
These examples each have the same three items in the market basket: apples, computers, and medical care. Initially, the respective weights are 0.4, 0.2, and 0.4.
In the high-inflation example, the price of apples rises 15% per year, computer prices are flat, and the price of medical care rises 20% per year. In the low-inflation example, the price of apples rises 3% per year, the price of computers falls 10% per year, and the price of medical care rises 7% per year.
The formulas for calculating the three types of price indexes are as follows:
CPI (fixed weight)=w11
p11 × p1t+w21
p21 × p2t+ · · · + wn1
pn1 × pnt
where w are the weights of the respective commodities (they sum to unity), and p are the prices of the respective commodities. In the subscripts, the first number continued
CASE STUDY 3.1 (continued)
(n) represents the 1st, 2nd, etc. commodity, and the second number (t) represents the year. Thus, for example, p21 would be the price of the second commodity (computers) in the first (base) year, and p2twould be the price of computers in the year for which the CPI is being calculated.
In the other formulas we use the symbol q to represent the quantities of the goods or services purchased.
IPC (implicit deflator)= q1t× p1t+ q2t× p2t+ · · · + qnt× pnt
q1t× p11+ q2t× p21+ · · · + qnt× pn1
.
CPC (chained price index)= q1t× p1t+ q2t× p2t+ · · · + qnt× pnt
q1t× p1,t−1+ q2t× p2,t−1+ · · · + qnt× pn,t−1. We now turn to some numerical examples to see how these indexes differ during periods of high and low inflation.
Case #1: High inflation
Year 1 Year 2 Year 3
Apples 2,000 @ $1 1,800 @ $1.15 1,600 @ $1.30 Computers 1 @ $1,000 1.25 @ $1,000 1.5 @ $1,000 Medical care 20 @ $100 20 @ $120 20 @ $140
CPI, year 2= 0.4 ×1.15
1.00 + 0.2 ×1, 000
1, 000+ 0.4 ×120
100 = 1.14.
CPI, year 3= 0.4 ×1.30
1.00 + 0.2 ×1, 000
1, 000+ 0.4 ×140
100 = 1.28.
The rate of inflation in the second year is 14%; the rate of inflation in the third year is 12.3%.
IPC, year 2= 1,800× 1.15 + 1.25 × 1,000 + 20 × 120
1,800× 1.00 + 1.25 × 1,000 + 20 × 100 = 5,720
5,050= 1.133.
IPC, year 3= 1, 600× 1.30 + 1.5 × 1,000 + 20 × 140
1,600× 1.00 + 1.5 × 1,000 + 20 × 100 = 6,380
5,100= 1.251.
The rate of inflation as measured by the IPC is 13.3% in the second year and 10.4% in the third year. Note in particular that the difference between the inflation rate as measured by the CPI and the IPC is 1.9% in the third year, substan-tially more than 0.7% in the second year. Generally, this difference grows over time.
continued
CASE STUDY 3.1 (continued)
The rate of inflation for the CPC, the chain-weighted average, is the same as the IPC in the second year, because the previous year is also the base year. For the third year we have:
CPC, year 3 over year 2= 1,600× 1.30 + 1.5 × 1,000 + 20 × 140 1,600× 1.15 + 1.5 × 1,000 + 20 × 120
= 6,380
5,740= 1.111.
Thus in the third year, the rate of inflation as measured by the CPI is 12.3%, by the IPC is 10.4%, and by the CPC is 11.1%. The CPC is probably the best measure of inflation; by any measure, the inflation rate is uncomfortably high during these years.
We now turn to the low-inflation scenario, where the relevant data are as follows:
Case #2: Low inflation
Year 1 Year 2 Year 3
Apples 2,000 @ $1 1,800 @ $1.03 1,600 @ $1.06 Computers 1 @ $1,000 1.25 @ $900 1.5 @ $800 Medical care 20 @ $100 20 @ $107 20 @ $114
Using the above formulas and performing the indicated arithmetic, we find that:
Inflation rate Year 2 Year 3
CPI 2.0 1.6
IPC 1.4 −0.1
CPC 1.4 0.7
In this case, we don’t know whether the price level is rising or falling in year 3, although the chain-weighted average inflation rate of 0.7% is once again the best measure. Note that if computer prices continued to decline at 10% or more per year, the IPC would decline by ever-increasing amounts in future years. That is one of the main reasons why the BEA switched from using implicit deflators to chain-weighted deflators in 1995.
3.3 Could the inflation rate be understated?
From the above comments, it might seem obvious that the CPI overstates the actual rate of inflation. Before 1994, that was clearly the case. However, the BLS has now implemented most of the recommendations of the Boskin Commission. In an
effort not to overstate the actual rate of inflation, it is possible that government statisticians have put several changes in place that now have the net effect of understating the rate of inflation.
Inflation is likely to be overstated when shifts in the market basket of goods and services are not correctly recorded, when quality improvements are under-stated or ignored, or when new products and services are not introduced into the price index in a timely fashion. These are all relevant factors, and since 1994 all of them have been addressed by the BLS. Following the same logic, inflation might be understated if consumers increase the proportion of their income spent on more expensive goods and services, if quality deteriorates instead of improves, and if the BLS fails to measure the price increases that are actually occurring. Also, the CPI could exclude or underweight the price of items that are rising more rapidly than the average rate of inflation. In recent years, the major culprit in this category has been medical care costs.
The weights of each of the individual components of the CPI are designed to equal the relative importance of each category of goods and services in the average market basket. In most cases, that is indeed the case. However, the one glaring exception to that rule is medical care. In 2000, the NIPA data show that medical care represented 17.5% of total consumption. Yet the weight of this category in the CPI is only 5.8%, or about one-third of the actual proportion. The discrepancy arises because most healthcare services are covered by insurance. Yet directly or indirectly, the consumer pays the bill.
If medical care costs rose at the same rate as other prices, this discrepancy would not be serious. Yet medical care costs are rising much faster than the rest of the CPI. Furthermore, and even more serious, the BLS understates the actual increase in medical care costs. Finally, the BLS methodology has been revised to capture the shift from higher-priced name-brand prescriptions to lower-priced generic drugs, but does not measure the shift when someone loses their health insurance and must pay much higher prices for the same prescriptions.
In 2001, according to the BLS, medical care costs rose 4.7%, while expenditures on medical care rose 6.5%. After adjusting for more intensive use of medical care and the general aging of the population, those numbers seem consistent. At the beginning of 2002, though, many large medical insurers announced price increases ranging from 12% to 20%, yet that increase was not reflected in the BLS statistics.
Suppose someone shifts from a branded prescription that costs $70 per month to its generic equivalent that costs $20 per month. That is a decrease in the CPI, and is correctly measured by the BLS. Now suppose, however, that no generic equivalent of that drug is yet available. The patient has been paying a $10 per month co-payment through health insurance, which is then canceled, which means he must now pay $70 per month for the same drug. That is a substantial increase in the CPI, but that shift is not measured by the BLS.
Taking all these factors into consideration, the reported contribution of med-ical care costs to the overall CPI was inflation during 2001 was 0.058 times 4.7%, or 0.27%. However, the actual amount spent on medical care was 17.5%
of consumption. Hence medical care costs actually contributed about 0.82% to the inflation rate in 2001, which means the official figure published by the BLS understated inflation by more than 0.5%, ceteris paribus.
The other area in which reported inflation is understated is housing costs. In the short run, the price of a house does not provide the best measure of housing costs, since it implies that someone who just bought a house would have much higher costs than someone who has lived in an identical house for many years. Just because the title changes hands on a given house should not boost the CPI. Because of this issue, the BLS attempts to measure how much the house would rent for if in fact it were rented out to the occupants instead of owned by them. That measure is not without its flaws, but need not be biased either up or down.
While these two series do not necessarily agree in the short run, over the long run, the rate of increase in the CPI for owner-occupied housing should be roughly equivalent to the rate of increase in housing prices. However, over the 1992–2001 decade, the median sales price of existing homes rose 4.2% per year, compared to a 3.2% increase in the shelter component of the CPI. Since that component accounts for 30% of the total CPI, that error would understate the actual rate of inflation by 0.3% per year.
Taking these two factors into consideration, the current inflation rate could be understated by as much as 0.8% per year. Even if some of the criticisms of the Boskin Commission that have not been fixed by the BLS remain valid, the current understatement of inflation is probably at least 0.5% per year. This understatement occurs in services; the CPI for goods is now adjusted properly for continuing quality improvement and the introduction of new goods.