Bureau of Labor Statistics > Consumer Price Index > Methods > Quality Adjustment

Refrigerator Regression Model

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.

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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.

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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