A new approach for constructing home price indices: The

pseudo repeat sales model and its application in China

Constructing More Reliable and Less Biased Quality-controlled Home Price Indices

In Chinese cities, we face two unique features in that country’s urban residential

market, features which also characterize development in many emerging market countries: 


1. New home sales account for an exceptionally large share of total

sales in China (87% in 2010) due to a growth rate in the economy and urbanization that in the case of China has been truly unprecedented in world history.

2. Housing development in many high-density cities, such as those in Mainland China, Taiwan, Singapore and many other Asian cities, occurs at a uniquely large scale and with a high degree of homogeneity in the units built within the typical residential ‘‘complex’’. In each complex, a number of buildings are constructed containing altogether hundreds or even thousands of units all having essentially the same location, architecture design, structure, appliances and finishes.

The two unique features enable us to develop a new type of model to capture the dynamics in housing markets - "pseudo repeat sales model" (ps-RS).

Background of China's urban housing market

Timeline of the Chinese housing market revolution


We propose a new matching criterion that we think is particularly appropriate for Chinese cities and other high-density cities where large-scale residential complexes dominate the urban housing development. 


The two major methods in the academic literature for addressing this challenge are the hedonic and repeat sales regressions


The proposed model is (in fact must be) a  hybrid repeat sales/ hedonic model of the type that has been demonstrated to have desirable features in the econometric literature, because the paired units in the ps-RS are not identical. The hybrid (hedonic) component of our model is small and relies only on variables for which good data can be easily obtained, because it only has to control for differences between units within the same building.

Step 1. Choosing matching space - complex, phase or building

An eligible matching space should meet the criterion that all transactions within it share enough similarities in location, community and physical attributes.

Step 2. Matching rule for generating "pseudo pairs"

The second step is to generate pseudo repeat sales pairs within the given matching space.


Step 3. Introducing a flexible ‘‘distance metric’’ criterion into the matching rule

A ‘‘distance metric’’ is used to identify the most ‘‘similar’’ transactions within a building across adjacent periods, to form a smaller number of pseudo-pairs, rather than making all possible combinations. As we are trying to model price evolution, it is straightforward to employ a measure of valuation similarity.

For each building, we estimate a hedonic price model with physical attributes and time (quarter) dummies (since this is a within-building hedonic regression. Given the distribution of the values of this distance metric across all the possible adjacent-period pairs, we set up a flexible matching criterion.


Model specification of ps-RS model

Standard hedonic model to construct a housing price index

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A differential hedonic regression (ps-RS model)


Index estimation

Estimate results of ps-RS model


Coefficients of two sets of dummies - number of bedrooms, floor number


We can see that the marginal contribution of the number of bedrooms to a home’s total value has a clear inverse U shape


All else equal, a housing unit with five bedrooms has the highest value, while those units that have less or more bedrooms are cheaper. 


The coefficients of floor number dummies also show a nonlinear pattern. The dummies of lower than 15 stories have negative coefficients, suggesting that a first-floor apartment is slightly preferred to a higher-floor one up until the mid-rise level. The premium on units above the 40th floor suggests that home-buyers will pay a premium for views in the newer buildings.

We prefer the building-version regression because it can mitigate the omitted variables problem to the highest extent. 

In order to make an apples- to-apples comparison between the ps-RS index and the standard hedonic index, we employ weighted least squares (WLS) to estimate a new complex-based ps-RS index whose hedonic attribute weights over time will be the same as those in the hedonic index.

Three ps-RS Indices and the Hedonic Index for Chengdu


We can see that the OLS and WLS complex based indices are almost the same, suggesting that hedonic attribute drift effects are not importantly different between the hedonic and the ps-RS indices.


However, both the hedonic and the complex-based ps-RS price indices may display a bias in their long-term trend growth rates. 


As discussed in previous sections, there are two broad categories of omitted variables – location attributes and physical attributes


Omitted hedonic variables can cause the hedonic price index to track either above, or below, the true quality-controlled long-term price appreciation rate. Omitted variables can also cause such bias in the ps-RS index, but less so the smaller the pseudo sample matching space, as more and more omitted variables are controlled for the narrower the matching space.

By construction, location attributes are very well controlled for in the ps-RS index, but more a concern for the hedonic index. The rapid urbanization in Chinese cities has meant that location attributes may be inevitably tending to be less favorable over time, in particular, as newer units are located farther away from the CBD. It is possible that not all of the locational effects can be completely captured or accurately measured in the hedonic attributes database.

On the other hand, with such rapidly rising per capita income in Chinese cities, it would seem likely that the new housing units have been incorporating more and more favorable characteristics in terms of the physical attributes within the units. Yet the hedonic database does not have any information about physical attribute quality improvement except for the size and number of rooms. In this case the hedonic index will tend to overestimate the rate of price growth.

Comparison of buidling version ps_RS indices with different distance metric thresholds


By regressing the within-pair price differentials onto the classical RS time-dummies and the relatively small and easily observed within-pair differentials in the housing units’ physical attributes, we are able to construct three versions of ps-RS price indices for new homes, with complex, phase and building as matching spaces, respectively.


These new ps-RS indices show good results in mitigating

the problem of omitted variables which can bias hedonic

index estimation. In particular, the building-version ps-RS index does the best job.

For the building-version ps-RS model, we further introduce a flexible distance metric criterion based on the absolute value of the within-pair difference of the predicted hedonic values. By setting this criterion one can deal explicitly and flexibly with the trade-off between the ‘‘purity’’ of the within-pair hedonic attribute homogeneity and the estimation sample size that can mitigate random error or noise in the index.

In summary, the ps-RS would seem to be an important new real estate price index methodology contribution particularly appropriate for rapidly urbanizing economies with high-density cities, such as in mainland China, Taiwan, Singapore and many other Asian cities (and in the future probably in South Asia and Africa).

Constructing real estate confidence index to predict housing price and new sales:

Investor Confidence as a Determinant of China's Urban Housing Market Dynamics

China’s urban housing market dynamics suggest that evolving investor confidence may be a relevant demand shifter. Such investors are continually updating their beliefs about the state of the macro economy and the policy uncertainty related to national and local housing policies. We build a 35 Chinese city real estate confidence index that varies over time and across cities. This index predicts subsequent house price appreciation and new housing sales. We document evidence of heterogeneous effects of investor confidence depending on a city’s demographics and the city’s elasticity of housing supply. Our results based on a new household-level expectations survey bolster the case that investor expectations are an important determinant of real estate price dynamics.

Hedonic housing price indices in eight major Chinese cities (as the representatives of the 35 major cities)


All else equal, richer people are more likely to own housing. Second, there is a group of young men who seek an apartment to raise their marriage prospects. China’s skewed sex ratios means that men seek to rise in status relative to other men to compete in the marriage market. A third factor determining ownership demand is the expectation of future price appreciation.


We document that our confidence index predicts subsequent house price appreciation and new home sales even controlling for a set of “fundamental factors.” The evidence suggests that this confidence index does contain additional information about the future path of housing market price and home sales. We also show that this index has heterogeneous impacts on local real estate outcomes. The association between the confidence index and housing market outcomes is further amplified in cities featuring a larger share of young men who are eager to buy homes to raise their marriage prospects. In cities with a more inelastic housing supply, we observe a larger positive correlation between our confidence index and local price increases.


Siqi Zheng
MIT China Future City Lab

Xiaoyang Guo
Hang Lung Center for Real Estate, Tsinghua University

David Geltner
Center for Real Estate, MIT

Hongyu Liu
Hang Lung Center for Real Estate, Tsinghua University

Web & Visual
Haijing Liu
MIT China Future City Lab

Icons from the Noun Project



Xiaoyang Guo, Siqi Zheng, David Geltner and Hongyu Liu. “A New Approach for Constructing Home Price Indices: The Pseudo Repeat Sales Model and Its Application in China”, Journal of Housing Economics, 2014, 25: 20-38. 


Siqi Zheng, Weizeng Sun and Matthew E. Kahn. “Investor Confidence as a Determinant of China’s Urban Housing Market Dynamics”, Real Estate Economics, 2016, 44 (4): 814-845.