New and existing homes, while different products with very different characteristics, are both part of the overall housing market. And depending on the state of the housing market, changes in underlying fundamentals can impact each differently.

For example, changes in the relative price of new-to-existing homes can cause substitution effects: Buyers may prefer new homes, but because of recent price increases choose to buy existing homes instead. Income effects may also be present, as changes in income could lead to increases in both new and existing home sales. One thing that is consistent across both categories, though, is the effect of inventory: Sales of both home types are limited by the available supply.

To account for these dynamics, we use a vector error correction model to forecast new and existing home sales. This model uses a system of equations to estimate a long-run relationship among housing market fundamentals. It then uses information about the deviations from the estimated long-run relationship and monthly changes in these fundamentals to predict the current state of the housing market. One advantage of this approach is that it also allows us to forecast the median sale price of each type of home within the same system.

Our forecast includes data on the following variables, representative of supply and demand factors in the overall housing market over the period starting in January 2001:

• Number of homes available for sale: Single-family, condo & co-op (SA)
• Mortgage principal and interest payments (SA)
• Housing construction: Completions – single-family privately owned (SAAR)
• Median sales price of existing homes: Single-family, condo & co-op (SA)
• New home sales: Median home price (SA)
• Total personal income (SAAR)
• Number of households (NSA)

All data are monthly except for the number of households, which is quarterly but interpolated to a monthly frequency. Mortgage principal and interest payments, total personal income and the number of households are combined to create a measure of monthly income per household used for mortgage expenses.

To estimate the model, we first estimate a vector auto regression and choose the number of lags using Akaike’s Information Criteria. We then estimate the long-run relationship among the variables in the system using the Johansen procedure.

After the model has been estimated, it is back tested using an expanding window to test the variables chosen in the model. The starting point is the first 80 percent of the data. The model is re-estimated using this shortened data set, and a one-period ahead forecast is obtained. One period is then added to the data set and the process is repeated. The out-of-sample accuracy is then used to determine which variables should be included in the system by adding and removing them successively to minimize the mean absolute percent error.