We use rental data from CMHC reported by census subdivision across Canada. CMHC’s rental data cover rental data for the entire universe of condominiums and does not take into account the tenure of the rents and only focus on the rental properties that are currently in the market. Our data range from 2006 to 2021. We also collect census data from Statistics Canada for a range of control variables in our models.

We estimate the following linear regression:

yi,t = β0 + β1xi,t−1 + γt + δz + ui,t

where the dependent variable yi,t is either average $ rent or vacancy rate for a two-bedroom condominium for census subdivision i and year t.

γt are year fixed effects, and δz are province fixed effects. xi,t denotes census subdivision-level economic and demographic characteristics; namely, the number of immigrants, non-permanent residents, interprovincial immigrants, and residents that work-from-home, working-age population, residents that are never married, using public transport, with bachelor’s degree and with college/CEGEP degree, as a share of census subdivision-level population; median income, unemployment rate, % in census subdivision-level population, the number of couples without children as a share of the number of households, and the number of unit completions as a share of the number of dwellings. All variables are lagged and at the beginning of each year. We cluster heteroskedasticity-robust standard errors by census subdivision.

Table 1. Variables and Descriptive Statistics

Table 2. Regressions of Rent and Vacancy

The table presents the regression results for for rents and vacancy by census subdivision from 2006 to 2023. Column (1) shows the complete regression results presented in Figure 1 and Column (3) shows the complete regression results presented in Figure 2 in the main report. Census subdivision-clustered robust standard errors are shown in parentheses. Statistical significance is denoted by: * p<0.1; ** p<0.05; *** p<0.01.

We project future rents using a neural network model. The neural network model implemented in this project is a Multi-Layer Perceptron (MLP) Regressor. This type of neural network is particularly suited for regression tasks, making it ideal for predicting continuous values. We use the Adam optimizer to minimize the loss function, which measures the difference between the predicted and actual values.¹ Additionally, an L2 regularization term is included to prevent overfitting, promoting better generalization to new, unseen data. The MLP Regressor iteratively adjusts its parameters in the layers to improve its predictive accuracy in training. After training, we use the model to project future rents by census subdivision for the years 2027 and 2032.

Based on the best predictors that we obtain from the linear model and factors that the Canadian Government makes projections such as immigration and population, we use the number of immigrants, non-permanent residents, and residents that work-from-home, residents that are using public transport and with bachelor’s degree, as a share of census subdivision-level population; median income, census subdivision-level population, and the number of unit completions as a share of the number of dwellings as the output variable in our neural network model to project future rents. We project non-permanent residents, immigrant levels, and population to better predict the 2027 and 2032 rents. We use Statistics Canada’s projections for these three variables.² Non-permanent residents and population have a projection for 2032, but immigrant levels projections only expand to 2026. So, we assume constant growth after 2026 up until 2032 for it. For other variables with no projections, we assume constant growth using historical data.

¹ For more details, please see https://arxiv.org/abs/1412.6980.

² For more details, please visit the hyperlinks: Non-Permanent Residents, Immigrant Levels, Population.