3.2 Results
3.2.5 The Modified Housing Price Model
In this section, the results of the housing price model regression with implemented synthetic lending rates will be discussed.
The Taylor rule was indirectly implemented in the housing equation through the lending rates. Thus, the lending rates were the main distinguisher between the modified housing price model and the actual housing price model. Lending rates were included in the housing price model through the variables user cost, interest rate and property tax rate, in addition to first-year payment. Hence, the process of creating the new housing price model was similar to the method of the previously estimated one, in which the variables that did not include either a short- or long-term lending rate were kept unchanged. However, the variables user cost, interest rate and property tax rate and first-year payment were altered.
To approximate the modified housing price model, the regression equation specified below was stated.
𝑙𝑜𝑔𝑃𝐻 = 𝛼0+ 𝛼1𝐷𝑙𝑜𝑔 (𝐾𝑃
𝑃𝐶𝑃) + 𝛼2(𝑆𝑦𝑛𝑡ℎ𝑅𝐸𝑁𝑇𝐸𝑀𝐼𝑁 + 𝑆𝑆𝐴𝑇𝑆 + 𝐴𝐹𝐷𝑅) +𝛼3𝐷(𝑆𝑦𝑛𝑡ℎ𝑅𝐸𝑁𝑇𝐸30 + 𝑆𝑆𝐴𝑇𝑆)𝐷𝐵98𝐾4
+𝛼4(𝑆𝑦𝑛𝑡ℎ𝑅𝐸𝑁𝑇𝐸30 + 𝑆𝑆𝐴𝑇𝑆 − 𝐷𝑃𝐶𝑃𝐸 − 𝐷𝑅𝐾𝑃𝐸) + 𝛼5(log (𝑌𝐷𝐻
𝑃𝐶𝑃) − log (𝐴𝐼𝐻)) + 𝜀
(Dam et al., 2011, p. 72).
All regression terms were kept unaffected except user cost ((𝑆𝑦𝑛𝑡ℎ𝑅𝐸𝑁𝑇𝐸30 + 𝑆𝑆𝐴𝑇𝑆 − 𝐷𝑃𝐶𝑃𝐸 − 𝐷𝑅𝐾𝑃𝐸)), interest rate and property tax rate ((𝑆𝑦𝑛𝑡ℎ𝑅𝐸𝑁𝑇𝐸30 + 𝑆𝑆𝐴𝑇𝑆)𝐷𝐵98𝐾4) and first-year payment ((𝑆𝑦𝑛𝑡ℎ𝑅𝐸𝑁𝑇𝐸𝑀𝐼𝑁 + 𝑆𝑆𝐴𝑇𝑆 + 𝐴𝐹𝐷𝑅)).
The OLS regression resulted in the estimate outcomes presented in the table in figure 14. Alterations in the individual variable coefficients and test results are outlined one by one in the following.
85
Figure 15: Housing price model with synthetic interest rates (authors’ own creation).
Lagged Change in Real Housing Price
The lagged change in the real housing price-variable was not revised after applying the synthetic interest rates to the model. Hence, the difference between the variable in the actual and the modified model was the coefficient value and the t-value caused by the renewed variable composition.
Identical to the results found for the actual model, the variable was highly significant at a 1 % level.
The coefficient changed from 0.558 to 0.615, and its t-value decreased slightly from 10.559 to 10.360. Concluding on the result, a change in interest rates had no substantial effect on the coefficient of the variable. As the imposed change did not affect this variable, the result of a similar estimation outcome was expected as this is in line with the OLS assumption of independent variables.
First-year Payment
The first-year payment variable described previously includes a short-term interest rate. Thus, this variable had to be modified in order to capture the effect of implementing the Taylor rate. A synthetic short-term interest rate replaced the original short-term interest rate, which led to a change in the coefficient value. The Taylor rate was on average below the market observed official bank rate throughout the entire estimation period, which led to a lower level of the synthetic short-term interest rate. Based on the result, a change in the short-term interest rate caused a less negative coefficient.
The coefficient in the new model changed from -1.886 to -0.255. Moreover, the t-value changed from -4.848 to -3.703. A lower interest rate induces a reduction in first-year payment. This, in turn, makes it cheaper to raise a loan and purchase a house. The impact on housing prices is, therefore, an upward trend, which is identical to a less negative change in the dependent variable. The result was therefore in line with fundamentals and economic instincts. Including a lower interest rate in the
Variable Name Coefficient Std.Error t-value p-value
Lagged change in real housing price Dlog(KP/PCP)- 1 0.61499 0.05936 10.360 <2E-16 ***
First-year payment (SynthRENTEMIN+SSATS+AFDR)- 1 -0.25476 0.0688 -3.703 0.00029 ***
Change in interest and property taxation rate (D(SynthRENTE30+SSATS)*DB98K4)- 1 -0.15372 0.07312 -2.102 0.03706 *
User cost (SynthRENTE30+SSATS-DPCPE-DRKPE)- 3 -0.17690 0.05483 -3.227 0.00151 **
Disposable income relative to housing stock (log(YDH/PCP)-log(AIH))- 6 0.04776 0.02921 1.635 0.10392
Constant 0.05196 0.03084 1.685 0.09392 .
Signif. Codes: 0.001 '***' 0.01 '**' 0.05 '*' 0.1 '.'
Estimation period: 1973Q1-2017Q2 R-squared: 0.4555 Adjusted R-squared: 0.4390 Change in Real Housing Prices - Modified Housing Price Model
86 model equation was expected to have a less negative influence on the housing prices than in the actual model. This becomes evident when reviewing the equation for first-year payment (𝑅𝐸𝑁𝑇𝐸𝑀𝐼𝑁 + 𝑆𝑆𝐴𝑇𝑆 + 𝐴𝐹𝐷𝑅).
The outcome of the Granger causality test displayed with a 5 % significance level that first-year payment Granger-causes changes is housing prices (see appendix S). This suggests that historical development in the level of first-year payment has important information in the explanation for the development in housing prices. The deviation in the Granger test outcome for this variable from the one in the actual housing price model might be explained by the implementation of the synthetic lending rate as the test is sensitive to changes in variable compositions. Nevertheless, the low power argument associated with this test is once again underlined.
Change in Interest and Property Tax Rate
The construction of the interest rate and property tax rate variable was similar to the construction in the actual model, but it was modified to include the synthetic long-term interest rate as a replacement of the actual rate.
The coefficient changed from -1.173 to -0.154 after implementing the synthetic long-term interest rate, and it appeared significant at a 5 % level. The modified variable induced a less negative effect on the housing prices compared to the pre-modified variable. When a lower lending rate is included as a consequence of the implementation of the Taylor-approximated official bank rate, the change in interest and property tax rate is reduced. This can be drawn from the equation specified for the variable, which is (𝑅𝐸𝑁𝑇𝐸30 + 𝑆𝑆𝐴𝑇𝑆)𝐷𝐵98𝐾4. A reduced interest rate level directly increases housing prices. This thereby explains the less negative variable coefficient. The comprised dummy implies that the variable is insignificant after the 4th quarter of 1998. Hence, some of the explanation for the large difference between the coefficient values in the two models may reasoned by the great deviations between the actual official bank rate and the Taylor rate prior to 1998. This is observable in figure 12.
A Granger causality test on the variable when including one lag, showed a p-value of 0.18. By including yet one lag, the null hypothesis was rejected at a 1 % significance level. This result illustrated how sensitive the Granger causality test can be. It is reasonable to assume that past
87 values of interest and property tax rate would include predictable content for explaining changes in housing prices. Periods of low interest rates affected the housing demand and consequently the housing prices positively, as discussed in the theory section. The effect of changing the interest and property tax rate today will affect future periods of housing demand and prices, according to the test results.
User Cost
The user cost variable is the last variable in the model to be affected by the implementation of synthetic lending rates. The coefficient changed from -0.20 in the actual model to -0.18 in the modified model. The result indicated that the effect of changing the long-term interest rate to a synthetic lending rate only to a certain extent changed the variable’s explanatory influence on housing prices. The alteration led the user cost to induce a less negative effect on housing prices.
This can be explained by the fact that a reduction in lending rates in accordance to the development the Taylor rule predicted, provokes a lower cost of owning a house, implying that more people are in the position of being a homeowner. This, in turn, stimulates an upward trend in housing prices, which is the same as a less negative effect.
In the evaluation of the relationship between user cost and housing prices, a Granger causality test substantiated economic foundation, as outlined previously, by proving that past values of user cost do contain useful information in predicting changes in housing prices.
Disposable Income Relative to Housing Stock
The last independent variable included in the housing price model specified by Dam et al. (2011) is the variable explaining the long-term effect on housing prices. The variable does not contain either the short- or long-term lending rate and was kept identical in the modified model.
To reach a statistically significant coefficient proved difficult in the estimation of the long-term variable in the modified housing price model. The variable was manipulated by adding lags in order to investigate if previous quarter’s values could increase the regressor’s explanation of housing prices.
This nonetheless did not lead to more feasible results. The variable had an identical coefficient as the estimate attained in the actual model of 0.05, as expected considering the independence condition in OLS estimations. Furthermore, the variable provided a p-value of 0.104, which indicated
88 that it was close to becoming significant within a 90 % confidence interval. For comparison reasons, it is worth mentioning that the coefficient value obtained in the actual model barely showed signs of significance at a 10 % level. Hence, it is argued that the long-term variable for disposable income relative to housing stock is not among the most predictive variables for housing prices, according to this thesis’ chosen model.
An insignificant disposable income relative to housing stock variable theoretically indicates that variable has no effect on housing prices, as the null hypothesis that the coefficient is equal to zero fails to be rejected. In practice, such a result often motivates omission of the variable. However, this thesis disregarded the fact that the variable was insignificant and chose to retain it in the model. This decision was justified by the fact that the variable was close to reaching an acceptable significance level. Besides, there exist conflicting arguments in the literature regarding whether to leave insignificant variables in the model or neglect them. According to Grace-Martin (2018), insignificant variables should be kept in the model if they serve a purpose. The disposable income in relation to housing stock variable is argued to serve a purpose as it explains the long-term relation and the supply of housing. Grace-Martin finalises the article by suggesting that the p-value provide one individual information measure and that a removal of insignificant variables solely based on this criterion may lead to a loss of important information (Grace-Martin, 2018).
Testing for Granger causality evidenced that disposable income relative to housing stock variable did not Granger-cause changes in housing prices. The reliability of this result can be discussed as past values of the long-term relation is most likely useful for forecasting changes in housing prices.
Historical supply of houses and disposable income is expected to influence the prices, based on economic reasoning. It can be argued that some of the explanation for the outcome can be supported by the insignificance of the variable.
The Constant
The result of the constant term in the modified housing price model had the same practical, yet inconsequential application as in the actual housing price model. Furthermore, it was not affected by the introduction of synthetic rates. The intercept’s coefficient estimate changed from 0.049 in the old model to 0.052 in the new. Besides, there was no change in its significance level.
89 Concluding Remarks
The result of implementing synthetic lending rates did not have a substantial effect on the coefficients or the significance of the variables. All coefficients retained their expected signs and the resemblance of the estimate values was striking. The increase in the coefficient of the interest and property tax rate variable yields the most distinctive change in coefficient value between the modified and the actual model.
The Granger tests conducted on the modified model indicated the presence of Granger causality between dependent and independent variables. The test also showed evidence of being highly sensitive to changes in lags in the new variables.
The process of conducting tests on the complete model was also carried out for the modified housing price model. A VIF test was applied to detect potential multicollinearity between regressors, whereas the Durbin-Watson was intended to detect autocorrelation in residuals. The result of these tests showed no signs of either case. The estimation results are attached in appendix P and R.
The number of influential outliers in the Cook’s D plot was greater than in the old model. However, the difference between the outliers’ values and the boundary was smaller compared to the actual model. The dummy-variable of 4th quarter of 1998 did not stand out as an influential outlier in the modified model as it did in the first estimated model. Based on observations of the plot, the largest outlier of the model occurred in the 4th quarter of 1974. This is the first observation in the dataset where the Taylor rate is implemented through the synthetic interest rates. One might argue that the effect of the first oil crisis in 1973 and 1974 may be reflected in the observation. Additionally, the economy was in the period from 1972 to 1979 vastly unstable. Volatile market condition for a longer time period makes the outlier as of the 4th quarter 1974 even less justifiable. Another significant outlier occurred in the 2nd quarter of 1987. One explanation for this observation’s Cook’s D value might be the new political initiatives, which was also identified in the actual model in section 3.2.1.
The new tax reform was implemented in 1987 and an introduction to a Potato cure in 1986 (“1987-skattereformen”, 2018). The ripple effect of the Potato cure in combination with the new tax reform may have resulted in making the observation as of 2nd quarter of 1987 more influential than others.
A Cook’s D plot for the modified model is found in appendix Q. Influential outliers may be tackled by omitting them from the model. However, as most of them are rationally reasoned in established
90 dataset specifications, the outliers were kept in the model. Consequently, the output result of the model was carefully assessed with this in mind.
Figure 16: Modified model compared with true housing prices from 1974Q4 to 2017Q2 (Statistics Denmark and authors’ own creation).