Per Capita Housing Starts: Forecasting and the Effects of Interest Rate

Transcription

1 1 David I. Goodman The University of Idaho Economics 351 Professor Ismail H. Genc March 13th, 2003 Per Capita Housing Starts: Forecasting and the Effects of Interest Rate Abstract This study examines the relationship between per capita housing starts and real interest rates. After examining the relationship between these variables, trend, seasonality, and ARMA analysis is used to forecast per capita housing starts. Finally, a discussion of how the variables interact with one another, how to better the forecast, and implications for consumers and developers are explored. Introduction Much research is dedicated towards explaining the relationship between interest rates and key economic indicators in the hopes of forecasting future economic conditions. An interesting feature for forecasting economic conditions are how housing starts reacts during different stages of economic growth. To better illustrate, Southwestern College states, The typical decline in interest rates during a recession reduces the cost of borrowing for households and businesses, and thus construction activity is usually an important early contributor to economic recoveries following recessions. Likewise if economic growth during the peak of the business cycle pushes up inflation, then the resulting rise in nominal interest rates will tend to reduce construction activity. Consequently a decline in construction activity may be one of the first indicators of a recession. (Southwestern College)

2 2 It is easy to understand why housing starts could increase during a recession. In an effort to offset a recession, the Federal Reserve can decrease interest rates, which in turn would lead to more housing since consumers can purchase housing at a lower interest rate. Moreover, a study by Scott Russell revels that the top reasons an economic dip will lead to more housing is inviting interest rates. (Russell 1) Thus, because of lower interest rates, it is more appealing for individuals to own houses instead of rent due to lower than average borrowing rates. Given this, many analysts concluded that among other factors, interest rates play the most significant role in deciding housing starts, that is, the housing supply is exceptionally sensitive to interest rates. (Painter, Redfearn, 1) To better illustrate, Frank Nothaft states housing is the most interest-rate sensitive sector in the economy, and each time mortgage rates drift lower [as a result of interest rates] it adds future stimulus to the industry. (Nothaft 1) Therefore, in analyzing an economy, interest rates play an important role in deciding the growth of housing starts. If interest rates decrease, housing starts should increase. On the other hand, if housing starts decrease, we should expect to see an increase in interest rates. Overall, by understanding this relationship, we can predict the housing market and it might also be an early indicator for major shifts in an economy. Thus, if one is able to accurately forecast housing starts and understand their relationship with interest rates, this could help in forecasting future economic conditions, which would in turn give developers and consumers insight as to the future of the housing market and economy. Therefore, it is the objective of this paper to understand the relationship between per capita housing starts and real interest rates and accurately forecast per capita housing starts.

3 3 Literature Review Although there doesn t exist a universal formula that models housing starts perfectly, Wojciech Szadurski, an economist from BMO Financial, states that there is a long-term relationship between housing starts and the adult population growth. In addition to adult population, he states that other non-demographic variables are important. These include growth in wood prices; growth in real personal disposable income per capita, changes in long-term interest rates, growth in real financial net worth, growth in real family income, the unemployment rate, the consumer confidence index, the growth in home prices relative to the Consumer Price Index (CPI), and the growth in rent costs relative to the CPI. He also states housing starts can be successfully modeled with information pertaining to the demand side of the market. This includes growth in real PDI per capita, changes in 10-year bond yields and the growth rate in housing prices adjusted for CPI inflation. (Szadurski 2) Other studies used models that include gross domestic product, consumer price index, producer price index, payroll employment, and interest rates to determine housing starts. (Interest Rate Forecasting 1) Overall, Southwestern College states that housing starts should increase with a decrease in interest rates, unemployment, and while consumer confidence and real disposable income increases. (Southwestern College 1) However, for this paper s purpose, we will ignore the other variables used in these studies and determine the extent to which per capita housing starts can be forecast by using previous history and then by their relationship with real interest rates.

4 4 Methods This study used two variables for forecasting the housing starts trend. They were per capita housing starts and real interest rates. Since the variable housing starts didn t reflect population, the variable housing starts was divided by population to get per capita housing starts. To determine the real interest rates, two variables were used. The first was the federal funds rate. However, this was in nominal terms so the federal funds rate was subtracted from the log of the consumer price index to get the real interest rate. Once this was done, forecasting was done using trend, seasonality and the Box- Jenkins AR (3) model. Also, analysis was given using the Granger Causality test, VAR analysis, and cross correlogram analysis. Finally, the impulse response function was analyzed. Data There were four sources of data used. They were all in monthly frequency and seasonally adjusted if possible. They were: 1) Population Mid-Month U.S. Department of Commerce: Bureau of Economic Analysis 2) Consumer Price Index For All Urban Consumers: All Items U.S. Department of Labor: Bureau of Labor Statistics 3) Effective Federal Funds Rate Board of Governors of the Federal Reserve System 4) Housing Starts: Total: New Privately Owned Housing Units Started U.S. Department of Commerce: Census Bureau

5 5 Discussion As mentioned in the introduction, per capita housing starts are highly cyclical and change according to various business cycles. Moreover, since the Federal Reserve often uses interest rates to impact different business cycles, we find that per capita housing starts tend to lag behind real interest rates. This makes sense, because consumers will build more houses given lower interest rates than higher ones. Figures 1 and 2 show the relationship of these variables over time and under different business cycles RINT Figures 1 & 2-The relationship of per capita housing starts and real interest rates over time. Given this, in an effort to create an unbiased forecast, a hold out and estimation sample was created. The estimation sample for our analysis is from 1959: :12 and the hold out sample is from 1996: :12. With this, we can now turn our attention towards the analysis. Figure 3 shows the autocorrelation function as well as the partial autocorrelation function for per capita housing starts. The autocorrelation function decays slowly and the partial autocorrelation function cuts off after displacement three. This along with the

6 6 Ljung-Box Q Statistic and probability reveal that they are statistically significant and aren t white noise. This also reveals that the data seems to be best represented by an AR (3) process. Figure 3-Correlogram of per capita housing starts Figure 4 shows the cross correlogram for housing starts and the real interest rate. The figure shows that both housing starts and the real interest rate are highly correlated at almost all the displacements. It also shows a definite pattern. One could interpret this to be that when person decides to build a house today, based on interest rates, it takes eight months to decided whether or not to build. This makes sense, since houses are a large

7 7 investment and it could take some time to decide whether or not to build given current interest rates. Figure 4- Cross correlogram of per capita housing starts and the real interest rate. Before a Granger Causality Test can be performed, the optimal VAR must be determined. Therefore, table 1 and figure 5 show the various VAR scores from 1 to 12. Because both SIC and AIC are minimum at lag length 7, this suggest that a VAR (7) model would best fit this data.

8 8 Lags SIC AIC Table 1-SIC and AIC scores for per capita housing starts and the real interest rate SIC AIC Figure 5-SIC and AIC scores for per capita housing starts and the real interest rate. Now that the optimum VAR has been determined, table 2 shows the results from the Granger Causality Test. In examining table 2, we reject the null hypotheses that the real interest rates don t cause per capita housing starts, and hold that real interest rates do affect per capita housing starts. More surprisingly, however, is that we hold the same for per capita housing starts. According to the Granger Causality Test, per capita housing starts also cause real interest rate. While this is counter intuitive, both could be related since housing starts and interest rates are both leading economic indicators. In any case, the causality is bi-directional and shows feedback.

9 9 Granger Causality Test Sample: 1959: :12 Lags: 7 Null Hypothesis: Observations F-Statistic Probability RINT does not Granger Cause E-06 does not Granger Cause RINT Table 2-Granger Causality Test for per capita housing starts and the real interest rate. Before forecasting per capita housing starts, the impulse response function must be examined. Figure 6 shows the impulse response function for per capita housing starts and the real interest rate at time period 10 and 250. After examining the impulse response function, we see that when the real interest rate is increased by one standard deviation, per capita housing starts decline dramatically for up to seven or eight years (100 periods). Also, when per capita housing is shocked, we see that real interest rate initially goes down for the first month but then increases until year three (40 periods) Response of to One S.D. Innovations Response of to One S.D. Innovations RINT RINT 0.8 Response of RINT to One S.D. Innovations 0.8 Response of RINT to One S.D. Innovations RINT RINT

10 10 Figure 6- Impulse response function of per capita housing starts and the real interest rate at time period 10 and 250. Finally, now that we have examined the relationship between per capita housing starts and real interest rate, we can focus on the forecast. Through regression analysis, we found that only seasonality and cycles exist in per capita housing starts. The Eviews regression outputs that lead us to this decision can be found in Appendices 4 through 10. Moreover, since the per capita housing starts correlogram in figure 3 pointed out an AR (3) model would be best be suited for forecasting, we will model after an AR (3) process. However, to make sure it was in fact an AR (3) process, we ran an ARMA (12, 12), MA (12), and an AR (12) regression to prove that AR (3) is the best fit model. The Eviews regression outputs can be found in Appendices 7 through 12. Table 3 shows the per capita housing starts regression with seasonality as an AR (3) process. This model shows that both the seasonality and the AR process are statistically significant, thus making this the best model. Also, since the adjusted R- square is high and the residuals in figure 7 appear to be white noise, it seems to be good for forecasting purposes. Finally, since the inverted AR root is.97, which is almost nonstationary, this could raise some caution. However, for this study we will ignore it and continue with the forecast.

11 11 Dependent Variable: Per Capita Housing Starts Method: Least Squares Sample(adjusted): 1959: :12 Included observations: 441 after adjusting endpoints Convergence achieved after 4 iterations Variable Coefficient StandardError T-Statistic AR(1) AR(2) AR(3) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Durbin-Watson stat Inverted AR Roots i i Table 3- Per capita housing starts regression with seasonality and as an AR(3) process Residual Actual Fitted Figure 7- Per capita housing starts residual graph.

12 12 Figure 8 shows the actual forecast, root mean square error and mean absolute error from time period 1996:01 to 2000:12. This forecast had a root mean square error of and a mean absolute error of , which overall, isn t that large. Figure 9 and figure 10 show the forecast against the actual values from the hold out sample. As shown in figure 9, the forecast captures the pattern of the data but over forecasts. The forecast also didn t pick up the beginning of the recession in However, overall, as figure 10 shows, the forecast does a good job of forecasting the overall long-term shape of per capita housing starts Forecast: F Actual: Forecast sample: 1996: : Included observations: 60 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion F ± 2 S.E. Figure 8-The actual forecast of per capita housing starts from 1996:01 to 2000:12.

13 F Figure 9a- Per capita housing starts forecast and actual values1994: : F Figure 9b- Per capita housing starts forecast and actual values 1959: :12. Conclusion As shown in the Granger Causality Test, real interest rates do in fact affect per capita housing starts. This information can be very useful for developers and consumers when trying to build a house. From examining the cross correlogram, given interest

14 14 rates, most consumers take up to eight months to decide whether or not to build a house. We also found that an AR (3) model with seasonality is the best univariant model to forecast per capita housing starts. Using this type of model allows the forecaster to capture the overall shape of per capita housing starts but with some errors as well. Therefore, if one is trying to forecast per capita housing starts without any error, a more complex model using methods discussed earlier in this study should be used. Appendix 1) Per Capita Housing Starts and Real Interest Rate Graph RINT

15 15 2) Per Capita Housing Starts and Real Interest Rate Cross Correlogram 3) Per Capita Housing Starts and Real Interest Rate Granger Causality Test Pairwise Granger Causality Tests Date: 05/15/03 Time: 10:55 Sample: 1959: :12 Lags: 7 Null Hypothesis: Obs F-Statistic Probability RINT does not Granger Cause E-06 does not Granger Cause RINT ) Per Capita Housing Starts Trend ls phs Dependent Variable: Method: Least Squares Date: 05/15/03 Time: 11:30 Sample: 1959: :12 Included observations: 444 Variable Coefficient Std. Error t-statistic Prob.

16 16 C E E R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) ) Per Capita Housing Starts Seasonality Dependent Variable: Method: Least Squares Date: 05/15/03 Time: 11:31 Sample: 1959: :12 Included observations: 444 Variable Coefficient Std. Error t-statistic R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Durbin-Watson stat ) Per Capita Housing Starts Trend and Seasonality @seas(10) Dependent Variable: Method: Least Squares Date: 05/15/03 Time: 11:31 Sample: 1959: :12 Included observations: 444 Variable Coefficient Std. Error t-statistic -6.98E E

17 R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Durbin-Watson stat ) Per Capita Housing Starts Correlogram 8) Per Capita Housing Starts AR (3), Trend, Seasonality @seas(10) ar(1) ar(2) ar(3) Dependent Variable: Method: Least Squares Date: 05/15/03 Time: 11:33 Sample(adjusted): 1959: :12 Included observations: 441 after adjusting endpoints Convergence achieved after 4 iterations Variable Coefficient Std. Error t-statistic -6.24E E

18 AR(1) AR(2) AR(3) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Durbin-Watson stat Inverted AR Roots i i 9) Per Capita Housing Starts AR (3) Seasonality ar(1) ar(2) ar(3) Dependent Variable: Method: Least Squares Date: 05/15/03 Time: 11:34 Sample(adjusted): 1959: :12 Included observations: 441 after adjusting endpoints Convergence achieved after 4 iterations Variable Coefficient Std. Error t-statistic AR(1) AR(2) AR(3) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Durbin-Watson stat Inverted AR Roots i i 10) Per Capita Housing Starts AR (12) Seasonality

19 19 ar(1) ar(2) ar(3) ar(4) ar(5) ar(6) ar(7) ar(8) ar(9) ar(10) ar(11) ar(12) Dependent Variable: Method: Least Squares Date: 05/15/03 Time: 11:35 Sample(adjusted): 1960: :12 Included observations: 432 after adjusting endpoints Convergence achieved after 3 iterations Variable Coefficient Std. Error t-statistic AR(1) AR(2) AR(3) AR(4) AR(5) AR(6) AR(7) AR(8) AR(9) AR(10) AR(11) AR(12) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Durbin-Watson stat Inverted AR Roots i i i i i i i i i i i i 11) Per Capita Housing Starts MA(12) Seasonality ma(1) ma(2) ma(3) ma(4) ma(5) ma(6) ma(7) ma(8) ma(9) ma(10) ma(11) ma(12) Dependent Variable: Method: Least Squares Date: 05/15/03 Time: 11:36 Sample: 1959: :12 Included observations: 444 Convergence achieved after 22 iterations Backcast: 1958: :12 Variable Coefficient Std. Error t-statistic

20 MA(1) MA(2) MA(3) MA(4) MA(5) MA(6) MA(7) MA(8) MA(9) MA(10) MA(11) MA(12) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Durbin-Watson stat Inverted MA Roots i i i i i i i i i i ) Per Capita Housing Starts AR (3) Seasonality ar(1) ar(2) ar(3) Dependent Variable: Method: Least Squares Date: 05/15/03 Time: 11:37 Sample(adjusted): 1959: :12 Included observations: 441 after adjusting endpoints Convergence achieved after 4 iterations Variable Coefficient Std. Error t-statistic AR(1) AR(2)

21 21 AR(3) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Durbin-Watson stat Inverted AR Roots i i F95 13) Per Capita Housing Starts and Real Interest Rate Lag Lengths ls phs c rint(-12) Lags SIC AIC

22 SIC AIC 14) Per Capita Housing Starts and Real Interest Rate Regression ls phs c rint(-1) Dependent Variable: Method: Least Squares Date: 05/14/03 Time: 14:04 Sample(adjusted): 1959: :12 Included observations: 503 after adjusting endpoints Variable Coefficient Std. Error t-statistic Prob. C E RINT(-1) -7.23E E R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic)

23 23 15) Impulse Response Function for Per Capita Housing Starts and the Real Interest Rate Response of to One S.D. Innovations Response of to One S.D. Innovations RINT RINT 0.8 Response of RINT to One S.D. Innovations 0.8 Response of RINT to One S.D. Innovations RINT RINT 16) Per Capita Housing Starts and the Real Interest Rate Regression Residuals Residual Actual Fitted