*Report available to the public as a courtesy of HousingEconomics.com
What happens to a new home’s market price if a builder decides to include an additional bathroom? NAHB has developed a model that can be used to estimate such price effects. The model, developed by applying statistical techniques to data from the American Housing Survey (AHS), has been updated several times over the years.  From the beginning it has consistently shown that an added bathroom has one of the strongest impacts of any home feature on single family detached home values.
This is also true of the most recent version of the model, which incorporates recently released data from the 2005 AHS. Looking at the bottom-line results from this model, a half bath adds approximately 10 and a half percent to a home’s value, and a full bath adds approximately 20 percent. But the story is a bit more complicated, and it’s necessary to go into the model’s results in more detail to fully understand them. Certain caveats about interpreting results from statistical models in general must be considered. And the percentage increase in home value varies somewhat, depending on other characteristics of the home, especially the number of bedrooms.
Economic theory, as well as plain common sense, suggests that the price of a house should be related to its characteristics. A home with a desirable amenity should, all else equal, sell for a higher price than one without the amenity. How much higher depends on demand for the amenity, the supply of homes possessing it, and the cost of retrofitting it in a home that lacks it. Given adequate data, it’s possible to estimate the implicit price for a particular feature—taking into account both how much it costs and how much people are willing to pay for it—controlling for other factors such as geographic location, neighborhood characteristics, and other features of the home.
As mentioned above, the model developed by NAHB to estimate these implicit prices is based on the AHS, a survey of about 60,000 nationally representative housing units that is funded by the U.S. Department of Housing and Urban Development and conducted by the U.S. Census Bureau in odd-numbered years. Due to limitations in the amount of geographic detail in the AHS, the NAHB model doesn’t estimate the price of a particular home in a specific neighborhood, but instead produces an average price for a single family detached home with particular characteristics across a broad Census region.
As a large government data base containing hundreds of variables, the AHS supplies considerable detail on the characteristics of individual homes and the neighborhoods in which they are located. A multiple listing service (MLS), which show homes for sale in a particular area, is another data source that sometimes provides considerable detail on housing characteristics. The AHS offers certain advantages, however, the primary one being that it provides consistent data across the entire country. MLS-based studies are typically only be done for a single metropolitan area. The AHS also contains a number of housing quality variables (for example, whether there are cracks in the walls) that are not in any MLS. On the other hand, some MLS data bases contain variables not in the AHS. Studies based on MLS and AHS data thus serve somewhat different purposes and are probably best viewed as being complementary to one another.
Having information on a variety of housing features is important when trying to control for other influences on house price and isolate the effects of a specific feature such as a bathroom. As Nancy Wallace of the University of California at Berkeley (among others) has pointed out, a statistical model can only provide accurate estimates of the prices of various features if the model incorporates all the important features of a home. 
Because a home is a complicated commodity with a large number of important features, this is an extremely challenging task. With diligence and care, however, the AHS enables us to come closer than other national sources of data, simply because the AHS provides more detailed information on housing characteristics. In deriving its model, NAHB spends considerable time experimenting with a large number of the home and neighborhood features available in the AHS. In general, features that show statistically significant impacts on home value are retained in the model. Features not included are checked to make sure that their removal doesn’t change other results materially to minimize omitted variable problems. 
Even in a data set as large as the AHS, this can’t be done perfectly. In the context of estimating the price of an extra bathroom, for instance, we might speculate that homes with a greater number of bathrooms also tend to have more elaborate bathrooms—for example, with features such as whirlpool baths or more than one sink. Because the AHS doesn’t collect information on whirlpool baths or multiple bathroom sinks, the statistical model can’t control for these characteristics. Were this speculation true, the estimated value of an additional bathroom would in part include the value of these extra amenities. The NAHB model seeks to estimate the value of an extra bathroom as precisely as is possible, controlling for the housing characteristics available in the AHS.
Based on the model and 2005 AHS data, Table 1 shows the percentage increases in value associated with added bathrooms. The table was constructed by taking standard two-, three-, and four-bedroom new homes, adjusting the number of full bathrooms and half bathrooms, using the NAHB model to obtain estimated values in different regions, calculating the average percentage change across regions, and rounding to the nearest half percent. According to the AHS, a full bathroom has a flush toilet, either a bathtub or shower, a sink, and hot and cold piped water. A half bathroom has hot and cold piped water plus one, and only one of the following: a toilet, bath, or shower.
The NAHB model is flexible in that it allows the impacts on home value to take different forms. The impact of full and half baths can be expressed approximately as a percentage of the home’s value, but the percentage will vary based on other characteristics, especially the number of bedrooms in the home. The model suggests that home buyers tend to prefer a rough balance between the number of bedrooms and the number of bathrooms. This means that if a home is out of balance in the sense of having more bedrooms than baths, adding an extra bathroom will increase the home’s value by a higher percentage.
When the number of bathrooms is approximately equal to the number of bedrooms, an additional half bath adds about 10 percent to the home’s value, and converting the half bath to a full bath adds another 9 percent, so one additional bath adds about 19 percent to the value. Below this (that is, when the home contains fewer bathrooms than bedrooms) the percentage gains associated with an added bathroom can be somewhat larger.
For example, starting with a home that has only one bathroom, an additional half bath will increase the value of a standard two-bedroom home by 11.5 percent, a standard three-bedroom home by 12.0 percent, and a standard four-bedroom home by 12.5 percent. The greater the disparity between beds and baths, the more there is to gain (in percentage terms) by adding an additional bath. One way to interpret this is that, when there is an excess of bedrooms over bathrooms, an additional bathroom makes the bedroom more valuable.
In different parts of the country, the percentage changes will translate into different dollar amounts. Table 2 shows the underlying house prices for a standard new home built in a suburban location in different regions of the county. Definitions of the standard homes are explained in the sidebar, and are based on median characteristics of new homes in the AHS data.
The AHS identifies the four principal census regions and the urban status (central city, suburb, and non-metro) of the area in which a home is located, but not the specific state or local jurisdictions. Information is available for some metro areas (generally aggregations of contiguous counties based on inter-county commuting patterns), but there are generally too few observations in any one metro to treat it separately. It is possible, however, to carve out a number of the larger California metros and treat them as their own "region" separate from the rest of the West.  House prices tend to be much higher in California than elsewhere in the West region. As Table 2 shows, the estimated price of a standard 3-bedroom new home with 1,850 square feet of living space, two full bathrooms, and no half bath is about $553,000 in a California suburb, compared to $308,000 in a suburb located somewhere else in the West.
For simplicity, the table shows estimated prices only for homes in suburban locations. The NAHB model also estimates prices for homes in central cities and outside of metropolitan areas. In most regions, the average house price in central cities is slightly below the suburban average. The average price outside of metro areas is much lower than in either the corresponding suburbs or central cities.
Note that, as you move from left to right across one of the rows in the table, the dollar increases in value associated with an added bathroom increase, even though the percentage changes tend to decline. For example, adding a half bath to a standard new two-bedroom, 1,700 square-foot single family detached home in a Northeast suburb with one full bath changes its value from $180,710 to $201,576. That’s an increase of $20,866, or 11.5 percent. Adding a half bath to an otherwise similar house with two full baths increases its value from $221,854 to $244,786. Although this is only a 10.3 percent change, it represents an increase in dollar terms of $22,932.
These dollar values are likely greater than the cost to builders of adding a typical bathroom. There are a couple of factors to keep in mind. One is that the model captures both demand and supply effects, so that the value of a particular feature depends on a combination of how much it costs and how much consumers desire it. More important is the aforementioned problem of trying to perfectly control for all other price influences in a commodity as complex as a house. Earlier the article mentioned the possibility that, in a home with a relatively large number of bathrooms, each bathroom might be larger and fancier than average. It’s also possible that the presence of additional bathrooms is correlated with other housing characteristics not captured in the model. If this is true, a bathroom is in part acting as a proxy for other characteristics, and the estimated value of a bathroom partially includes the value of characteristics the model is not controlling for.
This article has shown the estimated effect of additional bathrooms on the price of a new home in a suburban location. Readers interested in the effect of added bathrooms on the price of new homes in central cities or non-metropolitan areas, or on the price of older homes, or on homes with a different set of attributes, can explore these possibilities on the Internet.
The House Price Estimator can be run on any computer with a reasonably recent version of Microsoft Excel, if Excel’s security setting is adjusted to allow macros to run (that is, if security is set to “low” or “medium”). Users with little technical expertise or prior experience with Excel have reportedly found it easy to plug the various home features into the estimator and generate house prices with it.
 “Hedonic-Based Price Indexes for Housing: Theory, Estimation, and Index Construction” (PDF) Federal Reserve Bank of San Francisco Review, 1996. Return to Article
 For a technical discussion, see Jeffrey M. Woolridge, Econometric Analysis of Cross Section and Panel Data, 2002 pp 50-70. Return to Article
 The metro areas included in the California region are Bakersfield, Fresno, Los Angeles-Long Beach, Modesto, Oakland, Orange County, Riverside-San Bernardino, Sacramento, San Diego, San Francisco, San Jose, Santa Barbara-Santa Maria, Santa Rosa, Stockton-Lodi, Vallejo-Fairfield-Napa, and Ventura. Return to Article
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