5609.0.55.003 - Information Paper: Changes to the method of estimating loan commitments to first home buyers , 2015

ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 04/02/2015 First Issue

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Appendix

APPENDIX

1 This appendix documents the method used by the ABS to adjust the proportion of loans to first home buyers (FHB) to total loans (TL) for those lenders currently under-reporting to the Australian Prudential Regulation Authority.

2 The following States are currently affected: NSW, VIC, QLD, SA, TAS and ACT.

The Ratio Model has the lowest Mean Square Error among the tested models including both univariate and multivariate methods. It assumes that the FHBunaffected / TLunaffected ratio is not correlated with the model’s error term.

5 The Ratio Model is estimated for each State using data prior to the introduction of changes to FHB grant policy. The model results are then used to derive the estimates for future months.

PERIODS OF DATA USED FOR RATIO MODEL ESTIMATION


States	Periods
NSW	January 2002 to September 2012
VIC	January 2002 to June 2013
QLD	January 2002 to September 2012
SA	January 2002 to June 2014
TAS	January 2002 to June 2014
ACT	January 2002 to August 2013

Note: WA and NT are not affected at the time of the release of this Paper.

6 All model results are statistically significant. Among the presented models, the Ratio Model for ACT has the lowest R-squared (0.40) and the NSW model has the highest R-squared (0.89). Lower R-squared represents lower goodness of fit (i.e. how well the model fits the data).

7 The relative standard errors (RSEs) are derived from the Ratio Model’s standard error, which are provided in the model outputs.

8 The model’s R-squared and standard errors are summarised in the table below.


Ratio Model	NSW	ACT	VIC	QLD	SA	TAS

R-squared	0.89	0.40	0.81	0.86	0.68	0.65
RSE	0.015	0.033	0.017	0.015	0.017	0.026

9 The formula for calculating future proportions for each State and Territory is:

where

alpha1 : estimated coefficient for the intercept; alpha2: estimated coefficient for unaffected group proportion; alpha3 : estimated coefficient for the AR(1) term; t: time period

10 For example, the estimate for FHB/TL ratio for the affected provider group for NSW for October 2014 is:

12 This ratio can also be applied to the Total Loan value of the affected group to derive its FHB loan value, given that the Total Loan number and Total Loan value series have comparable trend properties and the average FHB loan size has been relatively stable since 2010.

Impact of policy change on FHB series

13 Data from the unaffected provider group in each State were used to estimate the effect, if any, of the change in FHB grant policy on the FHB series. This was done by using a dummy variable that distinguishes the periods before and after the policy change. This helps to detect any changes in the level of the series after accounting for its usual movement pattern.

14 Overall, the results do not suggest the change in grant policy has a statistically significant effect on the FHB series. The policy dummy coefficient is generally small (suggesting a fairly small effect on the FHB proportion) and only marginally significant for different States and Territories.

15 Structural break tests (the Chow Breakpoint test) were undertaken and showed no break for the FHB series (number of dwellings financed), but breaks for the ratio series ( % of all dwellings financed ) at the 10% level. This confirms the model findings above. These findings are based on the period from January 2002 to November 2014, of which the longest period after the policy change is only from October 2012 (i.e. for NSW and QLD).