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The Impact of Income, Base Rate, GDP, and Inflation(CPI) on Housing Price
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Assignment Task
Data and methodology
The data are from 1993 to 2023 at quarterly basis. the dependent variable is the house price and the independent variables are borrowers income, base rate, gross domestic product (GDP) and consumer price inflation (CPI).
OLS, using observations 1-124 Dependent variable: House Price UK
|
|
Coefficient |
Std. Error |
t-ratio |
p-value |
|
|
const |
−119108 |
11186.0 |
−10.65 |
<0> |
*** |
|
Income |
4.14377 |
0.223458 |
18.54 |
<0> |
*** |
|
Base rate |
−1675.70 |
586.341 |
−2.858 |
0.0050 |
*** |
|
gdp |
0.156880 |
0.0416389 |
3.768 |
0.0003 |
*** |
|
cpi |
637.089 |
137.348 |
4.639 |
<0> |
*** |
|
Mean dependent var |
200590.4 |
|
S.D. dependent var |
90603.49 |
|
Sum squared resid |
1.14e+10 |
|
S.E. of regression |
9803.258 |
|
R-squared |
0.988674 |
|
Adjusted R-squared |
0.988293 |
|
F(4, 119) |
2596.851 |
|
P-value(F) |
9.9e-115 |
|
Log-likelihood |
−1313.015 |
|
Akaike criterion |
2636.030 |
|
Schwarz criterion |
2650.131 |
|
Hannan-Quinn |
2641.758 |
|
|
|
|
|
|
The outcome of the multiple linear regression analysis is displayed in a Model 1.
House Pricet=β0+β1⋅Incomet+β2⋅BaseRatet+β3⋅GDPt+β4⋅CPIt+ut
House Pricet= -119108+4,15 * Incomet-1.675,70 BASE RATEt+0.157*GDPt+637,10*CPIt
The sign of all independent variables seems to behave as expected.
Namely:
- the positive coefficient on income suggests the direct correlation between greater incomes and higher house values
- the negative coefficient on the base rate indicates that there is an inverse relationship between interest rate and home prices meaning that higher interest rates are linked to lower house prices
- the coefficient for GDP and CPI is positively correlated indicated that stronger economic growth and inflation are associated with higher property prices
R2: the explanatory power of the model is high at (0.988674) meaning that the variability of the dependent variable (house price) is explained by 98.87% from the variability of all the independent variables (income, base rate, GDP, CPI).
Furthermore, the adjusted R2 =0.988293 is almost identical with the R2 and close to 1, meaning that it explains the variety of independent variables. The regression model has a good fit for the provided data.
The distribution of the residuals it seems not to have any specific pattern.
Auxiliary regression for RESET specification test
OLS, using observations 1-124
Dependent variable: House Price UK
| coefficient | std. error | t - Ratio | p-value | |
| const | 46611.1 | 31808.3 | 1.465 | 0.1455 |
| Income | 3.26793 | 0.908360 | 3.598 | 0.0005 |
| Baserate | −1857.67 | 880.822 | −2.109 | 0.0371 |
| gdp | 0.215065 | 0.0481324 | 4.468 | 1.83e-05 |
| cpi | −416.583 | 320.830 | -1.298 | 0.1967 |
| yhat 2 | 5.09529e-07 | 1.17613e-06 | 0.4332 | 0.6656 |
| yhat3 | 8.75609e-013 | 2.11508e-012 | 0.6796 | 0.6796 |
According to the outcome of the reset specification test, the null hypothesis is rejected, indicating that the model is not effectively explained may have an omitted, significant variable or a functional error non-linear equation. This implies that in the future, it will be essential to include additional variables.
Correlation coefficients, using the observations 1993:1 - 2023:4
5% critical value (two-tailed) = 0.1764 for n = 124
|
houseprice |
Income |
baserate |
gdp |
cpi |
|
|
1.0000 |
0.9916 |
-0.8069 |
0.9587 |
0.9361 |
houseprice |
|
|
1.0000 |
-0.8023 |
0.9509 |
0.9211 |
Income |
|
|
|
1.0000 |
-0.7391 |
-0.7188 |
baserate |
|
|
|
|
1.0000 |
0.9151 |
gdp |
|
|
|
|
|
1.0000 |
cpi |
Based on the Breusch- Pagan results the test statistic has a p-value of 0.722951 greater than 5%. By that we fail the reject the H0 of homoskedasticity meaning that the error variances are constant. The lack of heteroskedasticity indicates that the regression is well specified.
| coefficient | std. error | t-ratio | p-value | |
| Const | 9741.32 | 6619.33 | 1.472 | 0.1438 |
| Income | 0.107726 | 0.8174 | 0.8174 | 0.4153 |
| Base rate | −215.421 | 345.592 | −0.6233 | 0.5343 |
| GDP | -0.0.0251265 | 0.0245781 | −1.022 | 0.3087 |
| cpi | 30.6182 | 80.9092 | -0.3784 | 0.7058 |
| uhat1 | .818640 | 0.0545591 | 15.00 | 4.01e-029 |
Test statistic: LMF = 225.139313,
with p-value = P(F(1,118) > 225.139) = 4.01e-029
Alternative statistic: TR^2 = 81.358427,
with p-value = P(Chi-square (1) > 81.3584) = 1.88e-019
Ljung-Box Q' = 81.5948,
with p-value = P(Chi-square (1) > 81.5948) = 1.67e-019
Model 11: OLS, using observations 1993:1-2023:4 (T = 124)
Dependent variable: l_houseprice
|
|
Coefficient |
Std. Error |
t-ratio |
p-value |
|
|
const |
−9.06514 |
1.04260 |
−8.695 |
<0> |
*** |
|
l_Income |
1.20444 |
0.0560565 |
21.49 |
<0> |
*** |
|
baserate |
−0.0105707 |
0.00337625 |
−3.131 |
0.0022 |
*** |
|
l_gdp |
0.695447 |
0.123420 |
5.635 |
<0> |
*** |
|
l_cpi |
−0.174208 |
0.0693194 |
−2.513 |
0.0133 |
** |
|
Mean dependent var |
12.07344 |
|
S.D. dependent var |
0.564300 |
|
Sum squared resid |
0.357844 |
|
S.E. of regression |
0.054837 |
|
R-squared |
0.990864 |
|
Adjusted R-squared |
0.990557 |
|
F(4, 119) |
3226.506 |
|
P-value(F) |
2.8e-120 |
|
Log-likelihood |
186.6238 |
|
Akaike criterion |
−363.2476 |
|
Schwarz criterion |
−349.1462 |
|
Hannan-Quinn |
−357.5193 |
|
rho |
0.814331 |
|
Durbin-Watson |
0.357426 |
By applying the natural logarithm transformation, it is possible to linearize the relationship between the dependent variable and the independent variable. This transformation enables the coefficients to be interpreted as elasticities.
The logarithmic transformation can be used to stabilise the variance of the dependent variable and enhance the normality of the error components. These are crucial assumptions for ensuring the validity of statistical inferences.
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