1. Price Indices: Part 5 MEASUREMENT ECONOMICS ECON 4700

2. 2 This chapter Quality change Chaining

3. 3 Quality change The objective of the price index: To measure “pure” price change. Inspired by the Laspeyres index where you define a basket of goods and services and keeping it constant for a certain period. Compare the price of an item at two separate periods is useful if the quality of the items is constant (i.e. like-for-like using matched sampling). Otherwise: a quality adjustment is necessary in order to estimate the monetary value of the change in quality and adjust the price observation accordingly.

4. 4 Quality change The problem of quality adjustment arises when a product whose price has entered into computation of the index is replaced in the index by another and it is necessary to decide how much of any price difference between them should show up in the index as a price change.

5. 5 Quality change If there is no price difference the problem still arises, for the replacement may differ in quality. EC Regulation 1749/96 defines quality adjustment in Article 2(d) as the procedure of making an allowance for a quality change by increasing or decreasing the observed current or reference prices by a factor or an amount equivalent to the value of that quality change.

6. 6 Quality change It is clear that the index should fall both when prices fall and when existing product types get better. In either case, consumers obtain better value for their money and this should be reflected in the index whether it is a compensation index or an inflation index.

7. 7 Quality change Hofsten (1952) presents six situations: 1.The price is higher than before, but the quality has increased more than the price. 2.Both price and quality are higher, but the price has increased more than the quality. See this often when new varieties are introduced in the market. 3.The quality is higher but the price lower. 4.Both the price and the quality are lower, but the quality has decreased more than the price. 5.Both the price and the quality are lower, but the price has decreased more than the quality. 6.The price has increased and at the same time the quality has decreased.

8. 8 Quality change The situation At time 0 there is only one variety (a) and at time 1 this variety has disappeared and has been replaced by variety (b).

9. 9 Quality change Possible ways of handling quality change: 1.Direct comparison method I 01 = P b1 /P a0 : The replacement item is judged as equal to the old item Here any quality change is missed. If quality is improving and it is not being captured, then this imparts an upward bias on the index (vice versa). 2.Link to show no price change (splicing) All the price increase between the two periods is considered quality change and the index does not change: A = P b2 /P a1, where A is the quality adjustment factor. How is it done in reality:

10. 10 Quality change Lets assume at time 0 only variety a is on the market. At period 1 variety b comes onto the market while a is still there. At time 2, only variety b is available. How can we best measure the price development between 0 and 2? I 02 = P b2 /P a0 which is a direct comparison would not be a good measure of price change. You can link the two indexes (splicing method): I 02 = P a1 /P a0 x P b2 /P b1 … Will this give an acceptable result? In practice P a1 = P a0 and P b2 = P b1 so that I 02 = 1

11. 11 Quality change Assume oranges sold in periods 1 and 2 at $1.50/kg and that better oranges arrive on the market in period 1 and are sold for $1.75. In period 2, the oranges of the first kind have disappeared while the oranges of the second kind are still available at the same price. The splicing approach: (1.50 / 1.50) x (1.75 / 1.75) = 1 Implicitly was is being said is that all price increase is offset by an equal value improvement in quality. In other words the quality coefficient, g = P b1 / P a1 = 1.16 One would assume that in a free market, prices would adjust so that g = P b1 / P a1 is always true. EC regulations prohibit the use of this approach

12. 12 Quality change Suppose an incandescent light bulb delivers light at a cost of $10 per million lumen hours in year 0 and $12 in year 1, after which the old technology disappears from the market. Compact florescent bulbs appear in year 1, they produce light at $2.40 per million lumen hours in year 1 and at $1.80 in year 2. Assuming complete transition from the old to the new technology between periods then with the splicing technique: I 02 = I 01 x I 12 = (12/10) X (1.80/2.40) = 0.9 Note the old bulb is used for measuring the price change from period 0 to 1 are measured. Note the new bulb is used for measuring the price change from period 1 to 2 are measured. The linking procedure misses however the change in the fundamental price of the service as we move from the old to the new good = upward bias on the index The fact that revolutionary changes in technology have drastically lowered the cost of illumination gets lost in the linking.

13. 13 Quality change QA: Incidence of replacement DC: Direct comparison LSNC: Linked-to-show-no-change EJ: Expert judgement

14. 14 Quality change QA: Incidence of replacement DC: Direct comparison LSNC: Linked-to-show-no-change EJ: Expert judgement

15. 15 Other methods of quality adjustment 1.Option prices. 2.Production cost data. 3.Statisticians' judgments 4.Hedonic regressions.

16. 16 Option prices Where differences between the replacement product and the replaced product include features that were options in one of them, the price of these options can be used to provide a quality judgment of those differences.

17. 17 Production cost data In one or two countries, only for new cars, production cost data supplied by manufacturers adjusted by markup rates are used to derive retail values for the quality changes embodied in the annual model change.

18. 18 Added value features Lining to knee Describe any deviation from specification 100% Bamberg body lining Pure price change calculation Price difference (regular price of new product minus regular price of replaced product) 230.00 Estimated quality difference (new compared with replaced product) + 170. 00 Recommended pure price change + 60.00 Decreased value features Lining bound welted inside pockets Explain quality difference Bamberg lining / 4 Inside pockets / Better fabric / Excellent workmanship / Higher price point Substantiate any unusual recommended price change Features which specification requires to be recorded 2 button single breasted, 100% virgin wool, light weight, excellent workmanship, engineered construction, Jacket: 100% Bamberg body lining with 4 inside lining bound pockets, 3 cuff buttons with simulated buttonholes, Pants: front lined to knee, 3 pleats each side, lined zipper & crotch, waistband hook & eye & button. Judgement

19. 19 Hedonics A very attractive technique for dealing with quality change. Rarely used in practice except for computers and houses. Use multiple regression to relate the prices of an array of similar items, such as various computer models, to a number of their characteristics, such as ram, hd, monitor… The estimated coefficients provide implicit prices for each of the bundle of characteristics.

20. 20 Hedonics The form: P = a + b 1 X 1 + b 2 X 2 + b 3 X 3 + … + u a: constant X: characteristics (continuous or dummy) b: coefficients u: error term

21. 21 Hedonics Hedonics (Constant Quality Method) –Price of new homes are a function of their physical attributes. –Floor area, number of bedrooms, air conditioning, fireplace, etc. –The method assumes that with more sq. meters, more bedrooms, a fireplace, or more baths command a higher price. –In many cases the relationship can be assumed linear…

22. 22 Hedonics Hedonics (Cont’d) –…and thus can be illustrated with a linear equation: –Price = f(bedrooms, baths, fireplace) –Example: Price = m 2 x cost per m 2 + constant –Slope of curve is the rate per m 2 –Comparing cost per m 2 or the constant, allows the comparison of prices despite variations in size or other attributes. –Apples are compared with apples.

23. 23 Floor Space (m 2 ) Price ($) 20 000 40 000 60 000 80 000 10 000 Equation of line: y = mx + b Slope = 400 $/m 2 ( = 20 000/50) : Observed floor space m 2 : Predicted floor space m 2 $20,000 50 m 2 500 550

24. 24 Hedonics Equation : P = 400 X + 10 000 A 1000 m 2 house sold in period 0 (base) for $410 000 A 1200 m 2 house sold in period 1 for $500 000 This is not a $90 000 increase in price!!! NOT comparable… …BUT using hedonic… The predicted price of a 1200 m 2 house = 400 (1200) + 10 000 = $490 000 490 000 - 410 000 (base) = 80 000 => Quality change 500 000 – 490 000= 10 000 => “Pure” price change or Inflation = 420 000/410 000 = 2.4 % and NOT 500 K / 410 K = 22%

25. 25 Hedonics Problems –Data intensive –Can’t include all relevant variables – not available or not enough degrees of freedom –New features are a problem –Which functional form to use –Collinearity

26. 26 Chaining When an index is regularly revised, the index obtained by linking in successively revised indices end-to-end is termed a chain index. Chaining is estimating long term price changes as products of short term changes. Advantages to chaining: –Keeps your basket representative of recent purchasing patterns –Helps keep your products current. –Provides accurate measure of changes over short periods of time. –Reduces the substitution bias in the index (i.e., the spread between the Laspeyres and Paasche indexes is reduced.) –Enables procedural improvements to the CPI. Disadvantages to chaining: –It costs more (weights and two sets of prices and outlets) –The average of the chained sub-indexes is not necessarily equal to the chained average of sub-indices (not additive)

27. 27 Chaining Time1234 Price1.001.100.551.10 I 4/1 = 1.10/1.00 = 1.10 I(ch) 4/1 = I 2/1 x I 3/2 x I 4/3 = I 4/1 = (1.10/1.00) (0.55/1.10) (1.10/0.55) = 1.10

28. 28 Chain index