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QUALITY, QUANTITY, SPENDING �AND PRICES �

by�Kenneth W Clements and Grace Gao�Business School�The University of Western Australia

March 2012

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THE MYSTERY OF QUALITY

Fillet versus rump steak
Business class versus economy
Subjectivity
Quality of the whole consumption basket
Restaurant meals vs medical services
Quality is difficult

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QUALITY AND CONSEQUENCES

Computers
Cars
Household appliances
Mobile phones
“Pure” price changes – need to hold quality constant
Neglecting quality improvement understates volumes

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CURRENT APPROACHES

Price of product
Hedonics
Statistical agencies

Matched model
Package size: Price increases by x% and size by y%, adjusted price increases by x-y%
Hedonics: Computers, cars

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ISSUES WITH CURRENT APPROACHES

Subjectivity
Existence of “constant-quality” models
Quality of services
Quality of basket as a whole – differing units

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WHAT THIS PAPER IS ABOUT, I

Measure quality with luxury/necessity distinction
More affluent consumers spend relatively more on luxuries, less on necessities
Thus, luxuries are more desirable than necessities
Quality increases when consumption moves towards luxuries, away from necessities

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WHAT THIS PAPER IS ABOUT, II

Dimensionless concepts: Income elasticities and rates of growth of consumption
Applicable to the whole consumption basket comprising diverse goods and services
Quality index due to Theil

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WHAT THIS PAPER IS ABOUT, III

We introduce two new indexes:

(i) The “price” of quality, dual to the Theil index

(ii) Spending on quality

The three indexes (volume, spending and price) satisfy Fisher’s factor reversal test

New measures of the uncertainty of quality

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WHAT THIS PAPER IS ABOUT, IV

Application to 130+ countries from the ICP
Findings:

Quality increases with income, but at a slower rate
Luxuries are relatively more expensive in richer countries, necessities cheaper
80:20 rule

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QUALITY AND INCOME ELASTICITIES, I

Consider the deviation of the income elasticity from its weighted mean

Define the growth in real income as , so that relative consumption is

Suppose consumption of good i grows faster than average, so that . If this good is a luxury, and

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QUALITY AND INCOME ELASTICITIES, II

If i is a necessity and grows slower than average, then again

A positive value represents a movement towards a more desirable good, or away from a less desirable one
Quality of this part of the basket improves
Revealed preference measure of quality

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THE QUALITY INDEX

Theil’s quality index is a budget-share weighted average of the n terms

If , quality has increased
is a weighted covariance between the n income elasticities and the n quantity changes
When the two variables are positively correlated, quality improves

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SPENDING ON QUALITY AND ITS PRICE

An index of spending on quality is

Weighted covariance between the income elasticities and spending on the individual goods
The price of quality is

Weighted covariance between the income elasticities and prices

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FACTOR REVERSAL

Three indexes of quality:

The three indexes satisfy factor reversal test that

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INCOME SENSITIVITY OF QUALITY, I�

As , the quality index

can be expressed as

, where

is the income elasticity of quality

is a weighted variance of the income elasticities
when each

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INCOME SENSITIVITY OF QUALITY, II

Income elasticity of quality

For broad aggregates, likely to fall in range [0, 2], which implies

Thus, quality rises with income, but not as fast

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APPLICATIONS

ICP (2008) with 132 countries and n=12 goods
To compare country c with country d:

The three indexes then take the form:

Finite distances between countries mean that factor reversal now holds only approximately:

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INCOME AND FOOD BUDGET SHARE, VERSION 1�132 Countries in 2005

132. Congo

Income p.c.

US=100

Food budget share

(Percentage)

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INCOME AND FOOD BUDGET SHARE, VERSION 2�132 Countries in 2005

132. Congo

Food budget share

(Percentage)

Income p.c.

US=100

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SCATTER OF FOOD SHARE AGAINST INCOME

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Income per capita

Food share

(Percentage)

Source: Gao (2012)

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BUDGET SHARES AND INCOME ELASTICITIES �132 Countries in 2005�(Means)�

Commodity	Budget Share (Percentage)	Income elasticity
1. Food	27.1	0.66
2. Alcohol & tobacco	3.3	0.93
3. Clothing	5.3	0.96
4. Housing	14.7	1.04
5. Durables	5.2	1.07
6. Health	7.6	1.16
7. Transport	9.6	1.18
8. Communication	2.5	1.22
9. Recreation	4.9	1.36
10. Education	8.3	0.99
11. Restaurants	4.4	1.28
12. Other	7.1	1.30

Source: ICP (2008) and Clements and Chen (2010)

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COMPRESSING RESULTS

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BASE=US, I

Quality index:

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Move from left to right along horizontal axis, we compare US income with successively poorer countries
Thus, relative income rises
Quality also rises
Positive relationship is quite clear
Income elasticity is positive, but substantially less than unity (as expected)
It may seem to be counterintuitive that quality is a necessity, but it does agree with the previous analysis a couple of slides ago
This difficulty in enhancing the quality of the consumption basket may be an explanation of the apparent lengths to which consumers in rich countries are prepared to go to in the pursuit of ever more elaborate ways to spend their incomes
Veblen (1899) points to the apparent excesses of consumption of the rich in the US Gilded Era, 1890-1915, and coined the term “conspicuous consumption”
Robert Frank in his book Luxury Fever (1999) documents a surge in luxury spending in the US during the boom of the 1990s; this surge surely extended up to the financial crisis of 2007. He argues much of that spending was socially wasteful and cites colourful examples of $17,000 watches, sales of luxury cars, bigger and better equipped houses, pleasure craft, professional home appliances and cosmetic surgery.
This type of spending is indicative that it is not easy to enhance the effective quality of the consumption basket of the rich and the extraordinary “efforts” they have to incur to increase this quality.
This suggests a low income sensitivity of quality

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BASE=US, II

Price of quality:

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MULTILATERAL APPROACH, I

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is volume of quality in country c relative to all 132 countries

Compresses 8k+ pairs of countries into 132 parameters
Preserves skew symmetry
geometric mean=1

Restriction: Just row and column effects, no specific interactions due to role of groups of countries

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MULTILATERAL APPROACH, II

OLS estimator of in is

This is the closest single number to the 132 elements in the c^th row of
Standard error of quality allows inference (it’s a form of SIN)

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COUNTRY GROUPS

Still have 132 values of
Compress further by dividing the 132 countries into 6 income groups, each with 22 members
Group-wise version of above model is

quality in group g relative to world
, where
Consistent in aggregation

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Country group	Index	Group-wise comparison
Country group	Index	2. Medium rich	3. Lower rich	4. Upper poor	5. Medium poor	6. Very poor
1. Very rich	11.89	5.05	11.55	13.54	18.27	22.92
2. Medium rich	6.84		6.50	8.49	13.22	17.87
3. Lower rich	0.34			1.98	6.72	11.37
4. Upper poor	-1.65				4.73	9.38
5. Medium poor	-6.38					4.65
6. Very poor	-11.03

MULTILATERAL INDEXES

A. Volume of quality

(Logarithmic ratios )

Upper triangle of a skew-symmetric matrix

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Country group	Index	Group-wise comparison
Country group	Index	2. Medium rich	3. Lower rich	4. Upper poor	5. Medium poor	6. Very poor
1. Very rich	1.75	0.65	1.25	2.19	2.72	3.69
2. Medium rich	1.10		0.60	1.54	2.07	3.04
3. Lower rich	0.50			0.94	1.47	2.44
4. Upper poor	-0.44				0.53	1.50
5. Medium poor	-0.97					0.97
6. Very poor	-1.94

MULTILATERAL INDEXES

B. Price of quality

(Logarithmic ratios )

Upper triangle of a skew-symmetric matrix

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UNCERTAINTY

Uncertainty regarding quantities, budget shares and income elasticities
Demand system for country c

Simulate system with to give

Use these values to compute 1,000 values of the three indexes

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SIMULATED QUALITY INDEX

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Mean: 17.81

SD: 1.85

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2. Medium rich	3. Lower rich	4. Upper poor	5. Medium poor	6. Very poor

1. Very rich
2. Medium rich
3. Lower rich
4. Upper poor
5. Medium poor

From left to right

Increasing income distance
Quality becomes more different
Dispersion of distribution rises

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QUALITY AND INCOME DISTANCE �BETWEEN COUNTRIES �

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Distance

x

Probability

(quality in c > quality in c+x)

1 23 45 67 89 111 132

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0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

0.55

0.50

Example

All pairs of country with distance x=45 e.g. (1,46) (2,47)… (87,132)
1,000 trials for each pair
In 93.5% of cases, richer countries have higher quality
This proportion increases with x

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PROBABILITY OF QUALITY DIFFERENCES�A. US versus others�

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1

0.90

0.80

0.70

0.60

0.50

Probability

(US quality> quality elsewhere)

US vs. Lebanon

Income distance x=45
1,000 trials
Quality in US > quality in Lebanon in 943 trials

132. Congo

111. Cameroon

89. Cape Verde

67. Brazil

45. Lebanon

23. Italy

1. US

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PROBABILITY OF QUALITY DIFFERENCES�B. All pair-wise comparisons

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A VARIABLE INCOME ELASTICITY?

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SUMMARY

Measure quality on basis of luxury/necessity distinction
Use for whole consumption basket – diverse products
Price of and spending on quality
Both volume and price of quality increase with income (slowly)
80:20 rule

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