Introduction
The new housing price index (NHPI)Note measures the
change over time in builders’ prices of newly built houses
(single/semi-detached homes and townhomes). The NHPI is a monthly index available
for 27 cities.Note
To produce a constant-quality
price index, the NHPI uses a matched-model approach—wherein prices for the same
house models are compared over time—along with explicit quality adjustments. Data
are collected monthly from builders as part of a survey using an electronic
questionnaire. The house structure and land components are also indexed
independently using builders’ estimates collected in the survey.
The NHPI is used by economists,
academics, and the general public to monitor trends in the residential sector
of the construction industry. Within Statistics Canada, components of the
series are used in the calculation of some elements of the Consumer Price
Index. In addition, the series are used by the Canada’s System of Macroeconomic
Accounts for deflating the value of the national housing stock. Due to the
level of geographic detail provided and the sensitivity to changes in supply
and demand, the NHPI series are of particular interest to the real estate
industry for comparison with the resale market. The NHPI is also used by
building contractors, market analysts interested in housing policy, suppliers
and manufacturers of building products, insurance companies, federal government
agencies such as the Canada Mortgage and Housing Corporation (CMHC), and
provincial and municipal housing agencies responsible for housing policy.
1. Data
1.1 Sampling Process
To ensure that the NHPI continues to measure accurate
changes in prices, Statistics Canada subject matter specialists review each city’s
sample size to determine whether new builders need to be introduced on a
monthly basis. The sampling process uses a multi-stage sample design, where the
first stage is to select residential builders and the second is to select
representative models that will be priced over time.
1.2.1
Online Research
To aid in the effort of
increasing and maintaining the NHPI’s sample size, online research for new
builders is completed on a monthly basis.
Subject matter specialists make
use of publicly available data on builder websites which depict model
characteristics and occasionally prices for a given development to determine
whether a builder and its models are in scope and can be reasonably tracked
over time. If the builder is successfully initialised for the survey, the
builder receives a monthly electronic questionnaire to collect model and price
information.
1.2.2
Statistics Canada’s Building Permits Survey
An additional source for the
sampling frame is Statistics Canada’s Building Permits Survey. Builders are
selected, within a city, based on the value of their building permits. This
helps ensure that large tract builders that develop an entire subdivision are
included in the sample. Once a builder is identified as in scope, they select the
development they are building with the most lots available for sale within a
city and up to three of the top selling house models in this development. This
ensures that the same models can be followed over time within the same
development, and that these models are broadly representative of market
activity for new housing.
1.2 Prices
For the purpose of the NHPI, prices are defined as either
the transaction price or the list price for a model of a house as reported by
the builder in a given month, exclusive of any sales tax. This is the price
received by the builder, and excludes any additional fees paid by the buyer. A
model is the floorplan and features of the house structure.
1.2.1
Electronic Questionnaire – New Housing Price Report
The survey collects builders'
estimates of the current value (evaluated at market price) of the land. These
estimates are independently indexed to provide the published series for land.
The current value of the structure is also independently indexed and is
presented as the house series.
An electronic questionnaire is
used to collect price information for these models each month. If a model does
not sell in a particular month, the builder is asked for a list price. The
sample is periodically refreshed as developments sell out, and builders enter
and exit the market. The data collected from builders are manually reviewed for
consistency and completeness, and certain records are edited or removed based
on judgement.
1.2.2
Administrative and alternative data sources
Prices collected through this method are list prices as posted
on the builder’s website. Model characteristics such as square footage, number
of bedrooms and number of bathrooms is also captured. Online prices do not
include estimates of the house component only or land component only so they
are calculated using house to total and land to total ratios calculated from
previous year’s averages.
2. Index calculation
The NHPI is a matched-model index, and prices are stratified
by city, builder, and model to produce a price relative for each model that
each builder reports in the survey. The value of any promotions or upgrades is removed
from the price of a model prior to calculating a price relative. Provided that
house models do not change over time, this collection of price relatives has a
constant-quality interpretation. The price relatives for each model are then
aggregated to the city level using a Jevons index.
To make the index calculation
explicit, let be the price
of model by builder at time . These model prices
are used to calculate a price relative between period and period , , for each model that
each builder reports in the survey. To produce a city-level index, the price
relatives for all models by all builders are aggregated with a Jevons index
where
is the number of models
produced by builder , and is the number of
builders. This index is then chained with the previous period’s index value to produce an index running from the base
period to period .
2.1 Weights
Weights are estimated annually for each of the house
component, land component and the total for each city. Using collected
builders’ estimates of the current value of the house and land components,
house to total and land to total ratios can be calculated for each city using
an average of the reported estimates from the previous year.
The weights to further aggregate the city level indexes to
higher level geographies are derived from sales values for singles, semis and
row house collected from the Canada Mortgage and Housing Corporation’s Market
Absorption Survey. These aggregate indexes are then calculated using the Lowe
formula combining weighted city level indexes to regional, provincial and
national totals for each of the house, land and total price index series.
2.2 Model replacement
When a house model is no longer
for sale, or no longer representative, and if it is replaced by another model in
the sample, a back price for the replacement model is imputed in the first
period that it appears in the sample. This allows for a new model to be used in
the matched-model index calculation immediately. The imputation is done with a
linear regression (hedonic) model that relates house prices to observed
characteristics (see de Haan and Diewert (2013, chapter 5) for more details). A
model is calculated for each of the 27 cities. No imputation is made when a new
model is added to the sample without replacing an old model, nor when a new
builder is added to the sample.
Letting be the price of model by builder in period , the regression model
is based on a structural model for house prices
where is a (row) vector of
model characteristics, is a vector
of location characteristics, and
are builder and time
specific intercepts, respectively, and is an error term.
Housing characteristics include the log of lot size and house size (square metres),
and dummies for the number of garages and number of bathrooms. Location
characteristics include dummies for the property’s forward sortation area
(first three digits of the postal code).
The regression model is estimated
using a five year rolling window of data collected for the NHPI. Estimation is
done with a robust M-estimator, using the bi-square loss function (see Amemiya
(1985, section 2.3) or Wooldridge (2010, chapter 12) for more detail about
M-estimation). Under the assumptions of the classical linear regression model,
this approach to estimation is more robust to outlying price observations than
the usual OLS estimator.
When a new house model is
introduced into the sample, the characteristics for the new model and the
characteristics for the old model are used to calculate a pair of fitted prices
from the regression model. The fitted price for the new model is then
subtracted from the fitted price for the old model, and this difference is
added to the price for the old model to impute the back price for the new
model. This effectively accounts for the difference between the characteristics
of the old model and the new model, giving an imputation for what the price of
the new model would have been in the previous period. That is, plugging the
characteristics for a new model into
the hedonic model produces a fitted price , and plugging the
characteristics of the old model into
the hedonic model produces a fitted price . The difference
between these fitted prices is
then added to the price for the old model to produce a back
price for the new model .
The imputed price relative for the new model is then simply
and this is used directly in the
index calculation.
References
Amemiya,
T. (1985). Advanced Econometrics. Harvard University Press.
de
Haan, J. and Diewert, W. E. (Eds.). (2013). Handbook on Residential Property
Prices Indices (RPPIs). Eurostat.
Wooldridge,
J. (2010). Econometric Analysis of Cross Section and Panel Data (2nd
edition). MIT University Press.