With focus on six Southern California cities in three counties, city-average quarterly residential home prices are forecasted and the notion that home price movements in contiguous cities are contagious is investigated. The cities analyzed are Anaheim and Irvine in Orange County; Corona and Riverside in Riverside County; Redlands and San Bernardino in San Bernardino County. The forecasts are of each city’s average quarterly single family residential home prices for one year (starting the July-September quarter of 2013 and ending the April-June quarter of 2014). Historical data starting the July-September quarter of 2010 and ending the April-June quarter of 2013 are used to obtain the models that produce the forecasts. Forecasts of each city’s average quarterly prices were obtained using genetic programming (an artificial intelligence method). The forecasts suggest that prices will remain stable for most locations throughout the middle of 2014. Computations of elasticity coefficients suggest that home prices are rather responsive to mortgage rates (which are rising) and city unemployment rates (which are falling) lagged two to four quarters. The three year’s data investigated suggest little to no spatiotemporal price correlation between any contiguous pair of cities.
Recent improvements in economic conditions throughout Southern California seem to have had their effects on residential home prices. Over the past three years (12 quarters hereon referred to as Q1 to represent July-September 2010, Q2 to represent October-December 2010, …, Q12 to represent April-June 2013), the unemployment rate decreased in the six cities analyzed below. Between Q1 and Q12, the unemployment rate went from 12.5% to 7.9% in Anaheim (AH), from 7.0% to 4.6% in Irvine (IV), from 11.3% to 7.5% in Corona (CR), from 15.3% to 10.3% in Riverside (RS), from 10.9% to 7.5% in Redlands (RL), and from 19.6% to 14.0% in San Bernardino (SB). The effects of the improved local employment conditions on the local housing markets were assisted by the effects of the decline in the 30-year fixed mortgage rate (and therefore mortgage rates in general) from 5.1% in Q1 2010 to 3.47% in Q12. It is only reasonable to include the impacts of the improved local economic conditions and lower mortgage rates changes among the variables considered when modeling and forecasting residential home prices.
Using twelve quarterly average data (Q1 2010 through Q12 2013) as input, Genetic Programming (GP) is used to fit and forecast quarterly average home prices by city. GP is a computerized optimization random search technique that mimics regression modeling. The computerized algorithm selects the best set of explanatory variables out of a large set of variables to explain prior changes in home prices and produce linear or nonlinear best-fit mathematical models. GP produces a very large number of models that are compared with each other and the ones with the least mean squared fitness errors are carefully analyzed to identify the best forecasts.
Quarterly home-price variations (over the period from July 2010 through June 2012) for each neighborhood are explained by quarterly averages of each neighborhood’s home-characteristics (including average square footage of homes sold (SF), average number of bedrooms (BR), average number of bathrooms (BA), average ages of those homes (AGE), and a variable to account for average swimming pools (DVPL) where DVPL is a probability of having a pool. To capture the effects of changes in economic conditions on home prices, home prices are explained by lagged mortgage rates (MR) and lagged local unemployment rates (UR). MR and UR are each lagged two, three, and four quarters. The lengthy lags of changes in mortgage and unemployment rates logically impact residential home price changes at least three months after the changes occur and the effects may persist for up to one year. To determine and measure inter-city cross-price effects on each other, each city’s price equation includes its own lagged price as well as lagged prices from the other five cities.Here prices were lagged only one and two quarters assuming that the effects should be within six months of prior price changes. Model specifications representing all cities were similar and followed this same basic specification:
Pi,t=f(SFt, BRt, BAt, AGEt, DVPLt, MRt-2, MRt-3, MRt-4, URi,t-2, URi,t-3, URi,t-4, Pi,t-1, Pi,t-2, Pj,t-1, Pj,t-2) (1)
In equation (1), P is the average quarterly price of homes in a given location i at time period t where t = 1, …, 12 quarters, and the Pj represent average prices of any location other than location i (or for j ≠ i). The total number of variables given on the right-hand-side of (1) is 24. Although there are 24 right-hand-side variables GP can select from, it actually includes those variables that participated in changes of the dependent variable.And because there are no coefficients to estimate, there are no degrees of freedom lost. GP’s task is to search for the best model specification (linear or nonlinear) that produces best-fit defendable and logically reasonable results. Given the lag structure in equation (1), selected models would produce one-step-ahead forecasts. To produce forecasts for four quarters, one quarter-ahead forecasts for all six cities are obtained first and used as input to produce the following quarter. The process is repeated three other times to obtain a four-quarter forecast for each city. Further, fitted values of the dependent variables are then used to compute the needed elasticity coefficients. Estimates of those elasticity coefficients are presented after presenting each city’s price-forecasts below.
Over the twelve quarters (Q1 in 2010 and Q12 in 2013) investigated and used to obtain the GP models, average residential home prices in Anaheim increased by 13.8%. Here are the GP-selected variables that explained changes in the city’s prices over the three-year period:
PAH,t = f(SFt, AGEt, MRt-3, UR t-2, URt-3, URt-4, PCR,t-1,PIV,t-1) (2)
Figures 1(a) and 1(b) have the city’s average price and change in price history (Q1 – Q12) as well as the forecasts. Prices over the twelve-month forecast
period in Anaheim are expected to decrease by about 5%. Here are the quarterly forecasts for the city’s average home-price changes (where average SF = 1,670 and average AGE = 49.7):
Figure 1(a). Anaheim’s residential home prices
Figure 1(b). Anaheim’s home price changes
Bordering Anaheim and also in Orange County, over the same twelve quarters, Irvine’s average residential home prices increased by 5.1%. The following equation shows those variables that impacted the city’s price changes:
PIV,t = f(SFt, BRt, BAt, AGEt, MRt-2, MR t-4, PAH,t-2, P CR,t-1, PCR,t-2) (3)
From equations (2) and (3), it is clear that home-price changes of IV affect home-price changes in AH with a lag of one quarter and in turn AH’s home price changes affect those of IV with a lag of two quarters. Further and as equation (3) suggests, price-changes in the contiguous city of Corona affects both AH and IV. MR effects on AH and IV are present but with different lags. UR changes affect AH only. Finally, SF and AGE affect prices in both locations.
Figure 2(a). Irvine’s residential home prices
Figure 2(b). Irvine’s home price changes
Figures 2(a) and 2(b) have the Irvine’s average historical price changes as well as their forecasts. Over the forecasted one year, prices in Irvine are expected to increase by about 0.65%. Here are the quarterly forecasts for the city’s average home-price changes (where average SF = 1,880, BR = 3.28, BA = 2.5, and average AGE = 36.0):
Although in Riverside County, Corona borders Anaheim and Irvine in Orange County. Over the same twelve quarters (2010-2013), Corona’s average home prices increased by 9.0%. The following equation shows those variables that impacted the city’s price changes:
PCR,t = f(SFt, AGEt, DVPLt, MRt-2, MRt-3, MRt-4, URt-2, UR t-3, URt-4, PAH,t-1, PAH,t-2, PIV,t-1) (4)
Corona’s home prices are strongly impacted by economic conditions (MR and UR) as well as home prices in AH and IV. Figures 3(a) and 3(b) have the Corona’s average prices and price changes over the three-year period as well as the twelve months’ forecasts. Over the forecasted one year, prices in Corona are expected to remain unchanged. Here are the quarterly forecasts for the city’s average home-price changes (where average SF = 2,551, AGE = 17.6, DVPL = 0.18):
Figure 3(a). Corona’s residential home prices
Figure 3(b). Corona’s home price changes
Figures 4(a) and 4(b) have the Riverside’s average prices and price changes over the three-year period as well as the twelve months’ forecasts. Over the forecasted one-year period, prices in Riverside are expected to remain unchanged as well.
Figure 4(a). Riverside’s residential home prices
Figure 4(b). Riverside’s home price changes
Here are the variables that impacted the city’s price changes:
PRS,t = f(LSt, DVPLt, MRt-3, MRt-4, URt-2, PAH,t-1, P CR,t-1, PRL,t-2, PSB,t-2) (5)
The quarterly forecasts for the city’s average home-price changes (where average LS = 0.36 acre, DVPL = 0.23) are:
Located in San Bernardino County, Redlands’ twelve-quarter home prices and their one year forecasts are in Figures 5(a). Figure 5(b) has the plots of Redlands’ average price changes and their forecasts.
Figure 5(a). Redlands’ residential home prices
Figure 5(b). Redlands’ home price changes
Over the forecasted one-year period, prices in Redlands are expected to decrease by 3%. Here are the quarterly forecasts for the city’s average home-price
changes (where SF = 2,460, BR = 3.35, BA = 3.23, and DVPL = 0.27) followed by the equation showing the variables that impact Redlands’ prices:
PRL,t = f(SFt, BRt, BAt, DVPLt, MRt-2, MRt-3, URt-2, UR t-3, URt-4, PSB,t-1, PSB,t-2) (6)
VI. San Bernardino
San Bernardino’s prices are the lowest and most volatile in all six cities included in this study and are therefore expected to be the most impacted by economic conditions. The equation showing the variables that impact San Bernardino’s prices strongly suggests that mortgage rates lagged between two and four quarters are the driving variables. They are followed by the six-month lag of unemployment rate in the city. Here is the equation:
PSB,t = f(BAt, AGEt, DVPLt, MRt-2, MRt-3, MRt-4, URt-2) (7)
Figures 6(a) and 6(b) show San Bernardino’s average prices and price changes over the three-year period as well as the twelve months’ forecasts. Over the forecasted year, prices in San Bernardino are expected to decrease by 15% perhaps mostly due to the predicted changes in MR. Here are the quarterly forecasts for the city’s average home-price changes (where average BA = 1.66, AGE = 54, and DVPL = 0.12):
Figure 6(a). San Bernardino’s residential home prices
Figure 6(b). San Bernardino’s home price changes
For comparison purposes, Table 1 presents a summary of the forecasts presented above.
Computations from the equations obtained and reported above helped approximate various elasticity measures. Instead of representing each elasticity computation by a single value, each elasticity coefficient is estimated twice: Once when prices are rising and another when they are falling. The elasticity coefficients were computed to reflect changes as commonly reported in the media for the different variables. As these changes differ in size for these variables, the elasticity coefficients cannot be directly compared with each other to gauge relative economic impact of the various variables as explained below. The estimated coefficients are in Table 2.
Computations of the reported elasticity coefficients are not exactly conventional. Here are important distinctions that should be observed when interpreting the information in Table 2.
Because mortgage rate changes are mostly reported in increments of ¼%, the MR elasticity coefficients in Table 2 were computed as follows:
εMR,t= % change in Pi,t / ¼% change in MRt-τ (8)
Accordingly, if MR increased by ¼% during period(s) t-τ , where τ = 1, 2, 3, &/or 4 quarters, prices in location i would change by e MR,t. Thus and for example, if MR increased by ¼% in a prior quarter, AH home prices would decrease by 1.34%. Given the information equation (2)
provided, the lag is 3 quarters for AH.
Because unemployment rate movements are rather small (typically closer to ±1%), the UR elasticity coefficients reported were computed as follows:
εUR,t= % change in Pi,t / 0.1% change in URt-τ (9)
Else, all intercity-cross-price elasticity coefficients were computed as follows:
εi,Pi-Pj,t= % change in Pi,t /% change in Pj,t-τ (10)
The information presented in Table 2 helps make the following conclusions:
– MR effects are evident in all cities. The strongest effects of MR increases on home prices are in RL, IV, and AH. The strongest effects of MR decreases on home prices are in RL, IV, and SB.
– UR effects are also present in all cities. The strongest effects of UR changes on home prices are in RL.
– Intercity-cross-price elasticity coefficients are weak. The strongest is IV’s home price changes effect on AH’s future home prices (with elasticity revealing weak responses with estimates less than 0.4). Figure 7 has a map showing the bordering cities that barely impact each other.
– All estimated intercity-cross-price elasticity coefficients signs are as expected except for two: intercity-cross-price elasticity coefficients for RL between RS & RL and between SB & RL. The 1% increase in RS and SB prices should be logically followed by increases in Redlands prices.
The map in this report was prepared by Serene Ong, GIS Analyst, The Redlands Institute, University of Redlands.
Home-price data were obtained from Chicago Title Company. EZ2 Read Comps, 2010-2013.
Download the full report
About the Institute for Spatial Economic Analysis at University of Redlands
The Institute for Spatial Economic Analysis (ISEA) offers science and research based spatial analysis and forecasts of economic phenomena. ISEA serves regional, national and global communities in their needs to better understand how socio-economic phenomena affect and are affected by their communities and the space they live in. More information and previous ISEA publications can be found at http://isea.redlands.edu/.
You can follow ISEA on twitter @iseaRedlands.
Author: Mak Kaboudan, Mak_Kaboudan@redlands.edu
Professor of Economics & Statistics and ISEA faculty fellow,
School of Business, University of Redlands