Developing a Hedonic Regression Model For Refrigerators in the U.S. CPI
Nicole Shepler(1)
Background
The Bureau of Labor Statistics (BLS) is continuing research into extending the use of
hedonic regression models for quality adjustment purposes to additional items within the
Consumer Price Index (CPI). The CPI already uses hedonic models for apparel, televisions,
and personal computers. Recently, the CPI began using hedonic models for camcorders, VCRs,
DVD players, and audio products. Refrigerators were selected for hedonics research in
order to assess the use of hedonics on appliances.
Refrigerators are included in the Major Appliances CPI item stratum (HK01) along
with home freezers, washers, dryers, stoves and ovens, and microwave ovens. Refrigerators
have an estimated 33 percent of the weight within Major Appliances. During the time
period from December 1997 to December 1999 the Major Appliances index decreased 1.6
percent. Prior to December 1997, refrigerators were included in the Refrigerators and
Home Freezers (CPI item stratum 3001) index. This index rose 5.4 percent from December
1988 to December 1997.
Data and Regression Model
The existing CPI refrigerator sample was not sufficient for regression modeling
purposes. A supplemental sample of 390 observations was drawn by CPI statisticians. The
sample design for the additional observations was based on current CPI sampling
procedures. The final sample included 124 observations from the CPI sample and 214
specially collected observations for a total sample of 338 observations. The CPI data
collectors were unable to collect data for 45 percent of the supplemental sample due to
lack of respondent cooperation.
Overall, the quality of the data was quite good. Only 11 observations were deleted due
to inconsistent or incomplete information leaving 327 observations for use in calculating
the regression model. The marketing of refrigerators is reasonably straightforward — most
of the important price factors are easily observed. There was some confusion over
collecting some of the feature specifications. The information for many of these
specifications was obtained through secondary sources.
Refrigerators are a fairly homogeneous item. Virtually all of the refrigerators
available in today's market are frost free, have separate temperature controls for the
refrigerator and freezer, shelves built into the door, and so on. The most important
characteristics in a consumer's mind are size (capacity) and type (2). There are four
different types of refrigerators: one door (includes compact refrigerators); two door,
freezer on top; two door, side-by-side refrigerator/freezer; and two door, freezer on
bottom. For purposes of this study, the one door refrigerators were further separated into
two categories: one door, refrigerator only; and one door, refrigerator/freezer. Recently
more consumers are buying so-called unconventional refrigerators. These are high-end,
custom-made refrigerators that are built into existing kitchen cabinets and fit flush with
the adjacent cabinets. Also now available are flush freestanding units, which resemble the
custom-made units but with lower prices. The data collection form did not specifically
request whether a refrigerator was custom-made or flush freestanding and neither of these
characteristics were reported by the data collectors for any observations in the data set.
The model was specified with refrigerator types as independent variables and the
natural log of the most recent collected price was the dependent variable. Also, dummy
variables for sale price and Sub-Zero brand refrigerators were included as independent
variables. A sale price dummy was included since sale prices were reported for 38 percent
of the data. Comparing the mean sale price versus the mean regular price for each
refrigerator type found that the sale priced refrigerators were priced lower than the
regular priced refrigerators for all refrigerator types except for freezer on top
refrigerators. The means for sale priced and regular priced freezer on top refrigerators
were almost the same. A dummy variable for Sub-Zero brand refrigerators was included in
the initial model since a cursory review of the data found that those refrigerators had
much higher prices than the rest of the data. Sub-Zero is also marketed as a high-quality
upscale brand. The results of this preliminary model were as follows:
Variable Name
|
Parameter Estimate |
Standard Error |
T Statistic |
Tolerance Statistic |
Intercept |
7.166611 |
0.02341768 |
306.034 |
. |
Sale price |
-0.042403 |
0.02873232 |
-1.476 |
0.96762268 |
Sub-Zero brand |
1.482158 |
0.17717106 |
8.366 |
0.98857597 |
Two door, side freezer |
Base |
|
|
|
Two door, freezer on bottom |
-0.242652 |
0.09599466 |
-2.528 |
0.97716249 |
Two door, freezer on top |
-0.700635 |
0.02862091 |
-24.480 |
0.93439088 |
One door with freezer |
-2.077510 |
0.09628457 |
-21.577 |
0.97128693 |
One door, no freezer |
-2.408686 |
0.11351152 |
-21.220 |
0.97230647 |
R2 = 0.8119; Adjusted R2 = 0.8083; F Statistic = 230.150; Number
of Observations = 327
Since total refrigerator capacity was also believed to be an important price factor, a
regression model was run including this variable.
Variable Name
|
Parameter Estimate |
Standard Error |
T Statistic |
Tolerance Statistic |
Intercept |
5.484092 |
0.13081309 |
41.923 |
. |
Sale price |
-0.073300 |
0.02338826 |
-3.134 |
0.95762934 |
Sub-Zero brand |
1.119620 |
0.14615699 |
7.660 |
0.95258157 |
Total Capacity (in cubic ft) |
0.069560 |
0.00535103 |
12.999 |
0.18787927 |
Two door, freezer on bottom |
0.046569 |
0.08085690 |
0.576 |
0.90317621 |
Two door, side freezer |
Base |
|
|
|
Two door, freezer on top |
-0.343246 |
0.03595873 |
-9.546 |
0.38817940 |
One door with freezer |
-0.709558 |
0.13097047 |
-5.418 |
0.34423888 |
One door, no freezer |
-0.881981 |
0.14913992 |
-5.914 |
0.36935248 |
R2 = 0.8770; Adjusted R2 = 0.8743; F Statistic = 324.969; Number
of Observations = 327
Low tolerance values in the total capacity model indicate that multicollinearity is
present. Total refrigerator capacity is correlated with virtually all the refrigerator
type variables. The pearson correlation coefficients were:
|
Two door, side
freezer |
Two door, freezer on
top |
Two door, freezer on
bottom |
One door with
freezer |
One door, no freezer |
Total capacity in
cubic feet) |
0.66 |
-0.38 |
-0.03 |
-0.51 |
-0.49 |
The existence of multicollinearity was confirmed after comparing the two models.
Including the total capacity term caused the standard errors for the refrigerator type
parameter estimates to increase. Since the purpose of the hedonic model is to use the
actual parameter estimates for quality adjustments, the parameter estimates should be as
precise as possible. In this case, multicollinearity caused the parameter estimates for
the total capacity and refrigerator type variables to be imprecise. Therefore, a total
capacity variable and dummy variables for refrigerator type should not be included
together in the regression model. A graph of the natural log of price versus total
capacity shows that there is a strong linear relationship between the two (see figure 1).
The graph also shows that the total capacity variable could serve as a proxy for
refrigerator type. The one door, refrigerator only type refrigerators have the lowest
total capacity, and at the other end of the spectrum, the side by side
refrigerator/freezer type refrigerators have the highest total capacity. Therefore,
leaving refrigerator type out of the model should not bias the results of the regression
model.
A final model was specified as follows:
Variable Name
|
Parameter Estimate |
Standard Error |
T Statistic |
Tolerance Statistic |
Intercept |
5.053145 |
0.06344647 |
79.644 |
. |
Sale price |
-0.063669 |
0.01614744 |
-3.943 |
0.81814302 |
Total Capacity (in cubic ft) |
0.076640 |
0.00254559 |
30.107 |
0.33808126 |
Manufacturer/Brand: |
|
|
|
|
Sub-Zero |
1.259573 |
0.09805650 |
12.845 |
0.86185040 |
Kitchenaid |
0.197702 |
0.04966749 |
3.981 |
0.85560409 |
Crosley |
0.190145 |
0.06591812 |
2.885 |
0.76994994 |
Maytag |
0.141106 |
0.02501840 |
5.640 |
0.82145430 |
General Electric |
0.071763 |
0.02260078 |
3.175 |
0.64988988 |
Other brands not listed |
Base |
|
|
|
Frigidaire |
-0.117480 |
0.02846485 |
-4.127 |
0.79405576 |
Magic Chef |
-0.285150 |
0.07067682 |
-4.035 |
0.83460592 |
Abscold |
-0.344132 |
0.10015433 |
-3.436 |
0.82612388 |
Features: |
|
|
|
|
Bottom freezer |
0.258516 |
0.05400671 |
4.787 |
0.82443135 |
Sound insulation |
0.156196 |
0.02650773 |
5.892 |
0.83540986 |
Water filtration |
0.152287 |
0.02184786 |
6.970 |
0.51522445 |
Humidity controls |
0.087052 |
0.01688970 |
5.154 |
0.70688302 |
Three drawers (deli, meat, fruit and/or
vegetable) |
0.084151 |
0.01570547 |
5.358 |
0.81750318 |
Energy saver switch |
-0.060246 |
0.01893660 |
-3.181 |
0.77339235 |
Color |
|
|
|
|
White or Almond |
Base |
|
|
|
Black |
0.149743 |
0.03779698 |
3.962 |
0.92365705 |
Stainless steel |
0.322046 |
0.06840106 |
4.708 |
0.89106581 |
Wood panel |
0.452678 |
0.14298536 |
3.166 |
0.80815977 |
Ice Maker |
|
|
|
|
Installed ice maker and in door ice and water
dispenser |
Base |
|
|
|
Ice maker installed |
-0.109473 |
0.03063448 |
-3.574 |
0.59158297 |
Ice maker ready |
-0.122617 |
0.02468786 |
-4.967 |
0.47662241 |
No ice maker |
-0.135999 |
0.03076505 |
-4.421 |
0.38603477 |
Type of Outlet |
|
|
|
|
Full price appliance |
0.056029 |
0.01975203 |
2.837 |
0.56629278 |
Full price department |
Base |
|
|
|
Discount department |
-0.050380 |
0.02312863 |
-2.178 |
0.65427412 |
Discount appliance |
-0.094175 |
0.02659378 |
-3.541 |
0.72701315 |
Warehouse |
-0.349710 |
0.09530340 |
-3.669 |
0.91236339 |
Control Variables |
|
|
|
|
Western region |
0.072874 |
0.01806382 |
4.034 |
0.79058414 |
C-size city |
-0.083814 |
0.02867598 |
-2.923 |
0.69388832 |
B-size city |
-0.035407 |
0.01577656 |
-2.244 |
0.81045649 |
R2 = 0.9534; Adjusted R2 = 0.9488; F Statistic = 209.389; Number
of Observations = 327
Dummy variables for manufacturer/brand, miscellaneous features, color, ice maker, type
of outlet, and other control variables were added in addition to the sale price dummy
variable and total capacity variable.
The results of the model for the most part met a priori expectations.
Determining expectations for the manufacturer/brand variables was difficult if not
impossible. Several appliance manufacturers have "sub-brands" that attempt to
imply different levels of quality. For example, General Electric (GE) has GE Monogram, GE
Profile Performance, GE Profile, and GE. These GE sub-brands were all
classified as GE by the data collectors. Separating these sub-brands into individual
variables could have improved the specification of the model, but usually the higher-end
sub-brands have other quality factors that explain their higher prices. Another problem is
that some manufacturers make refrigerators that are then sold under a different
manufacturer's name. For instance, Whirlpool manufacturers KitchenAid and Roper brand
refrigerators in addition to the Whirlpool line. There were 22 different refrigerator
brands in the data set. Six brands (Amana, Fridgidaire, GE, Kenmore, Maytag, and
Whirlpool) accounted for 81 percent of the manufacturers/brands in the data set. Sub-Zero
refrigerators were mentioned earlier in the paper as being a strong price factor. As for
the rest of the manufacturers in the model, analysis of the parameter estimates does not
reveal any remarkable results. Kitchenaid, Crosley, Maytag, and GE all have positive
parameter estimates while Frigidaire, Magic Chef, and Abscold brands were all have
negative parameter estimates. In this data set, Magic Chef and Abscold refrigerators were
smaller and had fewer features.
A variable for bottom freezer refrigerator was included in the model despite originally
being classified as a refrigerator type. Refrigerators with bottom freezers are marketed
differently than the other types of freezers — many are custom made. They are typically
considered more upscale than the standard freezer on top or side-by-side
refrigerator/freezer models. This type of refrigerator is becoming more popular with
consumers and refrigerator manufacturers are planning on increasing their supply. The
bottom freezer variable also was not highly correlated with the total capacity variable
which allowed its inclusion in the model.
As for the other variables in the miscellaneous features category, the parameter
estimates for sound insulation, water filtration, humidity controls, and third
refrigerator drawer were all positive, while the energy saver switch had the only negative
parameter estimate. The parameter estimates for these miscellaneous features variables are
all consistent with assumptions.
- The sound insulation feature significantly reduces the noise the refrigerator makes
while it is running. This feature is achieved by a more sophisticated engineering design
process which pinpoints where more insulation is needed to reduce noise. These
refrigerators are also more energy efficient due to the extra insulation.
- A water filtration system filters out contaminants and odors from the water used in the
ice maker and water dispenser.
- Humidity controls regulate the humidity in the fruit and vegetable crispers. This allows
the fruits and vegetables to stay fresh longer.
- Three refrigerator drawers offers increased storage for types of foods that are
generally stored separately from the rest of the food.
- The energy saver switch was historically included on freezer on top refrigerators to
keep moisture from forming on the outside. Side by side and newer top mount refrigerators
have eliminated the need for this type of feature. Most refrigerators in today's market
have been engineered to automatically prevent the formation of moisture on the outside
(3). The negative estimate for this variable indicates that there are still some low
priced refrigerators with this feature.
Refrigerator color is also an important price factor. White, almond, or cream colored
refrigerators are the most common color in today's market. Other colors have become much
more fashionable in today's high tech kitchens. Some high-end refrigerators are now
available in black, stainless steel, or even paneled with wood. Many consumers are looking
to emulate professional kitchens where stainless steel is common. In a certain sense,
refrigerator color serves as a proxy for perceived quality. Therefore, it is not
surprising that the parameter estimates for black, stainless steel, and wood panel are all
positive.
All of the ice maker options were grouped together into a category. The most common
option in this data set was a combination of ice and water dispenser in the refrigerator
door with an ice maker. This option was designated as the base variable since it was
present in 49 percent of the sample. The remaining options were for an installed automatic
ice maker, ice maker ready (the customer has the option to install an ice maker), or no
ice maker. The resulting parameter estimates make intuitive sense.
Several variables were included in the model that control for type of business and area
of the country where the data are collected. These variables behaved as expected. The
negative parameter estimates for discount department, discount appliance, and warehouse
outlets are not surprising since these types of outlets are known for their low prices.
The parameter estimate for full price appliance outlets is positive. These outlets are
more service oriented and usually have higher quality merchandise than the discounters.
In preliminary model specifications, multicollinearity was problematic. However, in the
final model, the largest correlations (as measured by the pearson correlation coefficient)
were between total capacity and water filtration (0.45) and total capacity and no ice
maker (-0.55). These variables were kept in the final model since the correlations were
felt to be at an acceptable level. A high correlation between kilowatt hours used and
total capacity did preclude the inclusion of kilowatt hours into the final model. Kilowatt
hours of electricity used per year was believed to be an important price factor; however,
it is strongly related to total capacity since in general larger refrigerators require
more electricity.
Several variables which were expected to be price factors were not included in the
final model. The data collection form requested whether or not the outlet offers delivery
and the actual delivery charges. However, the data collectors had difficulty collecting
this information. Some of the data conflicted with other observations in the same outlet
and the data were not even collected for 44 percent of the observations. The type of
business variables capture some of the effects of the various delivery options. Variables
for warranty and country of origin also were not successful. For both of these variables,
there was not much variation. Most refrigerators (88 percent) were made in the United
States and country of origin was reported as "not available" for about 10
percent of the observations. Warranties for refrigerators were almost all reported as 1
year for parts and labor and 5 additional years for the compressor.
One possible improvement for a future refrigerator hedonic model would be the inclusion
of the energy star rating as a variable. According to the Energy Star website (4),
"energy star is a voluntary rating system established by the US Department of Energy,
the US Environmental Protection Agency and appliance manufacturers. Energy Star labeled
products surpass Federal energy efficiency standards by 20 percent of more." This
variable would be preferable to the kilowatt hours used variable since it is unlikely that
it would be highly correlated with any other variables.
Brand repair history could be tested in the future as a potential variable in place of
dummy variables for brand. This data could be obtained from an outside source such as
Consumer Reports magazine. This magazine did provide some refrigerator repair history data
in their June 2000 issue, but the data could not be easily applied to the data set used to
estimate the hedonic regression model (5). The Consumer Reports' data did not cover all
the brands that were in the regression model data set. As reported by Consumer Reports,
the brand with the worst repair history (for side by side models with ice makers and water
dispensers only) was Maytag. This brand was included in the regression model and had a
significant positive parameter estimate.
Index Results
In order to determine the impact of using the refrigerator hedonic model in the CPI, an
experimental Major Appliances index was calculated for the nine month time period
between July 1999 and April 2000. July was considered the "base" month — August
was the first month where the substitutions were reevaluated. The parameter estimates
obtained from the model were applied to refrigerator substitute items (an item chosen by
CPI data collectors to replace the previously collected item when it is no longer
available) with quality changes. There were 47 refrigerator substitutions over this time
period. In the published index, 76.6 percent had the price of the substitute item directly
compared with the price of the previous item. The price change for the remainder of the
substitutions was imputed via the class-mean imputation method (6). In order to calculate
the experimental index, the refrigerator substitutions were reassessed. Fifty-seven
percent of the substitutions were determined to have changes in quality that could be
adjusted using the hedonic model. Prices for the remainder of the substitutions were
directly compared. The substitution comparability ratio (the ratio of directly compared
and quality adjusted substitute quotes to the total number of substitute quotes) improved
from 76.6 percent to 100 percent! The majority of quality adjustments were to adjust for
changes in refrigerator total capacity. The table below summarizes the specification
changes that occurred with the substitutions.
Specification Change |
Number of
Occurrences |
Model number change and/or
other minor specification change |
18
|
Same item (actually not a substitution) |
2
|
Change in quality |
27
|
Quality Change |
Number of
Occurrences |
Total capacity* |
19
|
Humidity controls* |
8
|
Third drawer* |
6
|
Ice/water dispensers* |
7
|
Water filtration* |
7
|
Sound insulation* |
3
|
Brand* |
4
|
Energy saver switch* |
4
|
Color* |
1
|
* Note: more than one of these specifications could have changed for a
substitution.
From July 1999 to April 2000 the experimental index using the direct hedonic quality
adjustments increased the virtually the same amount as the published index (0.90 percent
for the experimental index versus 0.88 percent for the published). Chart 1 compares the
published versus the quality adjusted index and chart 2 compares the one month changes of
the published versus quality adjusted index. Although the effect of applying quality
adjustments to the Major Appliances index was negligible over the time period
examined, there were several noticeable differences in the one-month index change between
the experimental index and published index. The difference between the experimental index
and published index was largest during August and November 1999 and March and April 2000.
Quality adjusted refrigerator substitutions accounted for the highest proportion of
refrigerator substitutions during these four months — over 70 percent of the refrigerator
substitutions were adjusted for quality.
The unweighted mean price change for quality adjusted substitutions rose 2.56 percent
less than the unweighted mean price change for directly compared substitutions. The
directly compared substitutions were all very similar items (in some cases only the model
number was changing). This indicates that refrigerator retailers seem to be more willing
to raise prices on similar items. The table below compares the unweighted mean price
changes of the refrigerator substitutions.
Refrigerator Substitutions from August 1999 to April 2000
|
Published Index |
Quality Adjusted Index |
|
Number |
Mean Price
Change |
Number |
Mean Price
Change |
All substitutions |
47 |
2.07 % |
47 |
2.90 % |
Directly compared
substitutions |
36 |
2.29 % |
20 |
4.37 % |
Quality adjusted
substitutions |
0 |
. |
27 |
1.81 % |
Class-mean imputed
(noncomparable) substitutions |
11 |
1.36 % |
0 |
. |
The impact of applying the quality adjustments to the Major Appliances index was
negligible due to the small proportion of refrigerator substitutions in the index.
Refrigerators is just one of six items included in the Major Appliances index —
freezers, washers, dryers, stoves and ovens, and microwave ovens are also included.
Refrigerator substitutions accounted for 25 percent of the substitutions in the Major
Appliances index during the time period studied. On average, there were only five
refrigerator substitutions each month. The low counts for substitutions combined with the
low proportion of refrigerator substitutions in the overall index limits the potential
impact of using hedonics for quality adjusting refrigerator substitutions. One way to
increase the impact would be to direct the CPI data collectors to substitute more
frequently. This "directed substitution" approach is currently applied to the Personal
Computers and Peripheral Equipment (CPI item stratum EE01) index. Ideally, the data
collectors would be instructed to substitute at the time new refrigerator models are
available in an outlet. This would allow for more up to date items to be included in the
CPI sample. More substitutions would increase the potential for applying hedonic quality
adjustments to refrigerator substitutions and possibly lead to a greater impact on the Major
Appliances index. BLS is currently considering additional methods to allow for more
current items to be included in the CPI sample (8).
Notes:
(1) The author wishes to thank Charles Fortuna, Paul Liegey, and Mary Kokoski for
helpful suggestions.
(2) See Consumer Reports, June 2000, "Cold Choices", pages 41-45.
(3) See Maytag corporate website (www.maytag.com), as of March 6, 2000.
(4) See Energy Star website (www.energystar.gov/products/refrigerators/index.html), as
of March 6, 2000.
(5) See Consumer Reports, June 2000, "Cold Choices", pages 41-45.
(6) In addition to quality adjusting the refrigerator substitutions, some of the
imputed price changes for the class-mean substitutions (noncomparable substitutions) in
the Major Appliances index were recalculated since the inclusion of quality
adjustments changed the information used in calculating the imputations.
(7) See Marshall B. Reinsdorf, Paul Liegey, and Kenneth J. Stewart, "New Ways of
Handling Quality Change in the U.S. Consumer Price Index," BLS working paper no. 276
(Bureau of Labor Statistics. 1996).
(8) See Walter Lane, "Addressing the New Goods Problem in the Consumer Price
Index, "Presented at the Issues in Measuring Price Change and Consumption Conference,
Bureau of Labor Statistics, Washington, D.C., June 5-8, 2000, pages 1-26.
References:
Dennis Fixler, Charles Fortuna, John Greenlees, and Walter Lane, "The Use of
Hedonic Regressions to Handle Quality Change: The Experience in the U.S. CPI," 1999,
presented at the fifth meeting of the International Working Group on Price Indices.
Consumers Digest, November/December 1998, "Refrigerators and Freezers", pp
113-117.
Consumers Digest, November/December 1999, "Refrigerators and Freezers", pp
108-109.
Consumer Reports, August 1999, "Refrigerators", pp 46-49.
Consumer Reports, June 2000, "Cold Choices", pp 41-45.
Last Modified Date: October 16, 2001