Econometric Modelling of House Prices in Brisbane Essay Example

Econometric Modelling of House Prices in Brisbane

Unit Code

Linear Model

P_t = 5.504 – 1.72R_t + 0.001Y_t

The model indicates that the constant residential house price index for Brisbane is 5.504. This means that even if the mortgage rate (per cent per annum) and the state final demand are zero, the residential house price index for Brisbane would be 5.504.

The mortgage rate (per cent per annum) reduces the residential house price index for Brisbane by a factor of 1.72. If there is a unit increase in the mortgage rate (per cent per annum), the residential house price index for Brisbane would go down by 1.72, holding the state final demand constant. The reverse is also true. The sign is a true reflection of the state given that a rise in the mortgage rate would make it more expensive for buyers to take up the mortgage, and thereby reduce the demand for houses.

The state final demand raises the residential house price index for Brisbane by a factor of 0.001. If there is a unit increase in the state final demand, the residential house price index for Brisbane would go up by 0.001, holding the mortgage rate (per cent per annum) constant. The reverse is also true. The sign is a true reflection of the state given that higher demand is expected to cause a rise in the demand for houses.

The graph is a straight line rising from the left to the right, indicating that as the state final demand for houses in Brisbane goes up, the house prices also increase.

To test the individual significance of the slope coefficients, the computed t-ratio is compared to the critical t-ratio. Using the critical value approach,

:

:

Test statistic used is:

The test statistic is normally distributed with
degrees of freedom.

The table below summarises the individual significance of the slope coefficients.

Coefficient
Computed t-ratio (gretl)
Critical t-ratio ()
Comparison	-1.894 > 2.012	14.000 > -2.012
Null hypothesis
Conclusion	Significant	Significant

The confidence interval is given by;

Where
= mean,
= level of significance,
= standard deviation, and
= population.

-1.724 ± 2.012(0.910) = -3.555 , 0.107

P_t = 5.504 – 1.72(7)+ 0.001(80000) = 73.464

Log-Log Model

LogP_t = -7.482 – 0.014R_t + 1.118Y_t

The model indicates that the constant residential house price index for Brisbane is -7.482. This means that even if the mortgage rate (per cent per annum) and the state final demand are zero, the residential house price index for Brisbane would be -7.482.

The mortgage rate (per cent per annum) reduces the residential house price index for Brisbane by a factor of 0.014. If there is a unit increase in the mortgage rate (per cent per annum), the residential house price index for Brisbane would go down by 0.014, holding the state final demand constant. The reverse is also true. The sign is a true reflection of the state given that a rise in the mortgage rate would make it more expensive for buyers to take up the mortgage, and thereby reduce the demand for houses.

The state final demand raises the residential house price index for Brisbane by a factor of 1.118. If there is a unit increase in the state final demand, the residential house price index for Brisbane would go up by 1.118, holding the mortgage rate (per cent per annum) constant. The reverse is also true. The sign is a true reflection of the state given that higher demand is expected to cause a rise in the demand for houses.

The graph is a straight line rising from the left to the right, indicating that as the state final demand for houses in Brisbane goes up, the house prices also increase.

To test the individual significance of the slope coefficients, the computed t-ratio is compared to the critical t-ratio. Using the critical value approach,

:

:

Test statistic used is:

The test statistic is normally distributed with
degrees of freedom.

The table below summarises the individual significance of the slope coefficients.

Coefficient
Computed t-ratio (gretl)
Critical t-ratio ()
Comparison	-1.617 > 2.012	16.55 > -2.012
Null hypothesis
Conclusion	Significant	Significant

Using the critical value approach,

:

:

Test statistic used is:

The test statistic is normally distributed with
degrees of freedom.

Computed t-ratio (gretl) = 16.55

Critical t-ratio () = 2.410

Since 16.55
2.41, we reject the null hypothesis and conclude that Log(Y) is a significant predictor.

The confidence interval is given by;

Where
= mean,
= level of significance,
= standard deviation, and
= population.

1.118 ± 2.012(0.067) = 0.977 , 1.253

P_t = 5.504 – 1.617(7)+ 0.001(4.903) = -18.796

References

Freedman, D.H et al, 2007, Statistics, 4^th edn, New York, W.W Norton & Company.