Appendix B: Auxiliary Regressions | RDP 2014-03: Household Saving in Australia

RDP 2014-03: Household Saving in Australia Appendix B: Auxiliary Regressions

Richard Finlay and Fiona Price

April 2014 – ISSN 1320-7229 (Print), ISSN 1448-5109 (Online)

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B.1 Permanent Income Model

Since we cannot observe a household's permanent level of income, we estimate it by regressing current income on proxies for permanent income, including households' education level, occupation, marital status and age, and taking the fitted values as measuring permanent income (Table B1).

Table B1: Permanent Income Model
Coefficients
Variable	2003/04	2009/10
Education
– TAFE/certificate	0.0	0.1^***
– University	0.1^***	0.2^***
Middle-skilled occupation	−0.1^***	−0.1^***
Low-skilled occupation	−0.2^***	−0.2^***
Unemployed	−0.9^***	−0.7^***
Self-funded retiree	−0.7^***	−0.5^***
Pensioner	−0.6^***	−0.5^***
Not in the labour force	−0.1^***	0.1^***
Single-parent household	0.2^***	0.3^***
Married	0.5^***	0.5^***
Young	−0.1^***	0.0^*
Pre-retired	0.0	0.1^***
Old	−0.1^***	0.0^**
Constant	6.3^***	6.3^***
R²	0.49	0.39
Note: *, and * indicate significance at the 1, 5 and 10 per cent level, respectively Sources: ABS; authors' calculations

B.2 Risk of Unemployment Model

For households with a household head aged less than 65 years that had no persons unemployed at the time of the survey, the risk of unemployment variable is set equal to one if the fitted value of a logit regression of unemployment status on a range of household characteristics is greater than 10 per cent. In particular, for unemployed_it representing a dummy variable that equals one if household i has at least one unemployed person in survey t, and zero otherwise, we model unemployed_it using a number of independent variables including geographical location, wealth, age, migrant status, personal debt status and other relevant household characteristics, as detailed in Table B2.

Table B2: Risk of Unemployment Model
Coefficients
Variable	2003/04	2009/10
Better off than a year ago	−0.16	−0.67^***
Worse off than a year ago	0.26	0.11
Financially constrained	0.44^**	0.87^***
Number of credit cards	−0.23^***	−0.05
Personal credit status	0.49^**	0.58^**
Wealth-to-income ratio	0.00	0.01
No of spare rooms	−0.25^**	−0.15
Mortgage	−0.30	−0.46^**
Own home outright	−0.40	−0.77^**
Education – TAFE/certificate	0.26	0.26
Education – university	−0.01	0.40^*
Single-parent household	0.70^**	1.06^***
Married	−0.16	0.84^***
English-speaking migrant	0.46	−0.16
Non-English-speaking migrant	0.40	−0.02
Young	0.04	−0.12
Pre-retired	0.16	0.73^***
Old	0.75	−0.40
Vic	0.09	0.37
Qld	−0.12	0.19
SA	0.24	0.23
WA	0.08	0.14
TAS	0.18	0.02
ACT and NT	0.15	−0.81^**
Non-urban	0.25	0.11
Household size	0.67^***	0.57^***
Female	0.34^**	0.30
Share of children	−2.97^***	−1.79^***
Share of old	−2.46^***	−3.08^***
Constant	−4.17^***	−5.18^***
R²	0.13	0.15
Note: *, and * indicate significance at the 1, 5 and 10 per cent level, respectively Sources: ABS; authors' calculations

B.3 Median and Mean Regression Models

Tables B3 and B4 present full median and mean regression outputs. Each table shows outputs from three different models: Models (1), (2) and (3). The only difference between the three models is the measure of income used: the logarithm of current income is used in Model (1); the deviation of current income from permanent is used in Model (2) (this is the model used in the main text); and no measure of income is used in Model (3). Note that all variables used in the permanent income model are also included in the main saving model, so that Models (1) and (2) will have the same explanatory power and the same coefficients on variables not included in the permanent income model.

Table B3: Median Regression Model
Coefficients
Income (>20%)
Variable	2003/04			2009/10
	(1)	(2)	(3)	(1)	(2)	(3)
Worse off than a year ago	−2.2	−2.2	−6.3^***	0.4	0.4	−3.5^**
Income	0.6^***	0.6^***	na	0.6^***	0.6^***	na
– Business	−0.2	−0.2	2.6	−3.5	−3.5	−1.7
– Salary	3.4	3.4	16.6^***	3.3	3.3	12.6^***
– Government	8.6^***	8.6^***	−2.2	14.5^***	14.5^***	−0.4
– Other	0.6	0.6	−4.4^*	−5.4^**	−5.4^**	−7.5^***
Financially constrained	4.0	4.0^*	1.9	3.7	3.7	1.9
No of credit cards	−4.3^***	−4.3^***	−1.4^**	−4.1^***	−4.1^***	−0.8
Personal debt	−7.0^***	−7.0^**	−15.9^***	−6.0^**	−6.0^**	−17.2^***
Wealth-to-income ratio
– Young	−0.4	−0.4	0.3	−0.5	−0.5	0.2
– Middle-aged	−0.3^**	−0.3^**	0.0	−0.5^***	−0.5^***	0.0
– Pre-retired	−0.4^***	−0.4^***	0.0	−0.1	−0.1	0.0
– Old	−0.2^**	−0.2^**	0.0	−0.2^***	−0.2^***	0.1
Mortgage
– Young	1.3	1.3	3.6	2.4	2.4	0.3
– Middle-aged	−1.0	−1.0	2.6	5.7^*	5.7^*	4.7
– Pre-retired	−8.5^*	−8.5^**	0.5	−8.9^***	−8.9^***	−1.3
– Old	−17.4^*	−17.4	−0.1	−4.4	−4.4	−8.1
Own home outright
– Young	8.3	8.3	8.3	9.0	9.0	11.3
– Middle-aged	3.3	3.3	10.2^***	5.9	5.9	11.9^**
– Pre-retired	−6.8^*	−6.8^*	3.1	−4.2	−4.2	1.9
– Old	−12.7^**	−12.7^**	−5.7	−3.5	−3.5	−0.7
Gearing ratio
– Young	−9.0^**	−9.0^**	−13.8^**	0.9	0.9	7.4^*
– Middle-aged	−10.1	−10.1	−6.4	−7.7	−7.7	−6.0
– Pre-retired	−17.0	−17.0	−7.2	−1.7	−1.7	−10.9^*
– Old	−19.6	−19.6	−21.3	−11.6	−11.6	−5.5
Education
– TAFE/certificate	−3.7^**	−2.6	−3.5^**	−0.1	3.2^*	2.2
– University	−11.0^***	−4.3^**	−5.4^***	−5.3^***	4.3^**	0.6
Risk of unemployment	1.9	1.9	4.5^*	0.1	0.1	−1.7
Middle-skilled occupation	0.2	−7.1^***	−7.2^***	4.8^***	−3.2	−2.3
Low-skilled occupation	2.9	−7.8^***	−4.8^**	6.4^***	−3.3	−1.4
Unemployed	0.7	−48.9^***	−15.5^**	6.9	−33.7^***	−8.7
Self-funded retiree	−9.2^***	−13.6^***	−13.4^***	−5.8^*	−1.5	−2.1
Pensioner	4.6	−30.5^***	−6.1	4.0	−26.2^***	−2.9
Not in the labour force	9.7^**	−29.8^***	−4.0	6.4^*	−22.5^***	−1.3
Single-parent household	−15.6^***	−3.1	9.7^**	−10.1^***	8.4^***	7.9^***
Married	−12.2^***	15.4^***	−1.8	−10.6^***	17.9^***	−1.7
Non-English-speaking
migrant	6.2^***	6.2^***	2.0	7.4^***	7.4^***	2.8^*
Young	−0.7	−5.1	−0.4	−0.9	−2.4	0.1
Pre-retired	10.0^**	9.6^***	3.0	4.4	7.8^**	9.3^***
Old	15.1^**	6.7	13.4^**	7.3	4.6	12.9^**
State
– Vic	0.9	0.9	−0.7	2.9	2.9^*	−0.2
– Qld	1.7	1.7	1.0	2.7	2.7	0.7
– SA	5.1^***	5.1^**	1.4	9.1^***	9.1^***	6.5^***
– WA	2.0	2.0	1.1	3.9	3.9^*	3.8
– TAS	2.7	2.7	−2.1	5.5	5.5^**	−2.0
– ACT and NT	−6.4^***	−6.4^***	−2.8	−3.9^*	−3.9^*	6.3^***
Non-urban	4.3^***	4.3^***	0.3	4.5^***	4.5^***	−0.8
Household size	−11.3^***	−11.3^***	0.8	−10.1^***	−10.1^***	2.8^**
Female	−0.5	−0.5	−4.0^**	−0.7	−0.7	−3.3^**
Share of children	27.5^***	27.5^***	−15.9^***	9.6^*	9.6^*	−25.0^***
Constant/year effect in 2009/10	−318.9^***	35.6^***	6.8	−11.1	−14.5^**	−8.3
R²	0.15	0.15	0.05	0.15	0.15	0.05
Notes: *, and * indicate significance at the 1, 5 and 10 per cent level, respectively; HES household weights used; 500 repetitions of bootstrapped weights are used to obtain the standard errors; reference household is a single middle-aged male, born in an English-speaking country, not financially constrained, same or better standard of living compared with a year ago, working in a high-skilled occupation, with high school as highest level of education and lives in urban NSW Sources: ABS; authors' calculations

Table B4: Mean Regression Model
Coefficients
Income (>20%)
Variable	2003/04			2009/10
	(1)	(2)	(3)	(1)	(2)	(3)
Worse off than a year ago	1.0	−2.0^*	−5.4^***	−2.0^*	0.9	−3.2^***
Income	0.6^***	0.5^***	na	0.5^***	0.6^***	na
– Business	−2.0	4.5^**	7.5^***	3.0^*	−0.8	3.6^**
– Salary	5.6^***	8.9^***	14.9^***	6.3^***	7.5^***	6.8^***
– Government	15.5^***	5.6^***	−8.4^***	6.1^***	15.2^***	−1.2
– Other	−4.2^***	−4.5^**	−11.0^***	−2.0	−5.5^***	−13.7^***
Financially constrained	1.3	4.4^**	0.3	4.7^**	1.3	−1.3
No of credit cards	−3.9^***	−3.7^***	−0.6	−3.8^***	−3.8^***	0.2
Personal debt	−10.4^***	−10.6^***	−19.9^***	−10.6^***	−10.3^***	−21.5^***
Wealth-to-income ratio	−0.3^***	−0.4^***	−0.1^*	−0.4^***	−0.3^***	0.1^**
Mortgage	0.4	0.2	2.7^*	−0.1	0.4	3.4^**
Own home outright	3.4^**	2.4	6.3^***	2.2	3.1^**	5.6^***
Gearing ratio	−2.6	−10.8^***	−14.8^***	−10.3^***	−2.8	−8.1^***
Education
– TAFE/certificate	−0.4	−0.5	−1.6	−1.2	2.7^**	3.3^**
– University	−6.8^***	−1.8	−3.9^***	−9.0^***	4.8^***	2.3^*
Risk of unemployment	3.5^***	6.0^***	6.7^***	5.9^***	3.6^***	1.6
Middle-skilled occupation	4.1^***	−9.0^***	−6.5^***	0.4	−5.3^***	−1.7
Low-skilled occupation	5.7^***	−9.3^***	−5.9^***	2.6	−5.1^***	1.3
Unemployed	0.3	−43.7^***	−19.1^***	−1.3	−26.8^***	−15.9^***
Self-funded retiree	−4.0^**	−13.4^***	−8.2^***	−8.4^***	−7.9^***	−0.7
Pensioner	1.3	−27.4^***	−1.3	7.9^**	−35.2^***	−8.1^***
Not in the labour force	−1.8	−25.4^***	−4.7	9.2^***	−17.8^***	−4.1
Single-parent household	−6.7^***	−2.7	9.1^***	−10.2^***	4.7^**	5.3^**
Married	−7.2^***	12.5^***	−2.3	−11.7^***	18.4^***	−1.0
English-speaking migrant	−3.7^**	−3.8^**	−1.3	−4.5^***	−4.5^***	−0.8
Non-English-speaking migrant	5.2^***	5.1^***	2.1	7.7^***	7.8^***	5.4^***
Young	0.4	−4.5^***	0.0	−0.5	−3.5^***	2.7^**
Pre-retired	−1.3	0.9	−1.8	0.7	6.6^***	3.0^**
Old	5.8^*	−0.2	0.8	0.7	3.5	4.3
State
– Vic	0.5	0.4	−0.5	1.9^*	2.0^*	−2.4^**
– Qld	0.8	0.9	−1.0	1.6	1.6	−0.5
– SA	2.4	2.2	−0.4	10.0^***	10.1^***	5.5^***
– WA	2.9	3.0^*	0.3	2.1	2.1	1.9
– TAS	1.8	1.6	−1.8	4.6	4.5	−2.6
– ACT and NT	−4.6	−4.5	−1.9	−3.4	−3.3	4.3
Non-urban	4.4^***	4.6^***	0.4	3.5^***	3.4^***	−0.1
Household size	−10.4^***	−10.5^***	0.2	−9.9^***	−9.9^***	2.2^***
Female	−1.3	−1.4	−4.5^***	−0.9	−1.1	−3.0^***
Share of children	22.1^***	23.0^***	−14.3^***	8.5^***	9.4^***	−26.1^***
Constant	−315.1^***	32.9^***	8.5^**	−339.9^***	23.6^***	2.6
R²	0.15	0.15	0.05	0.15	0.15	0.05
Notes: *, and * indicate significance at the 1, 5 and 10 per cent level, respectively; HES household weights used; 500 repetitions of bootstrapped weights are used to obtain the standard errors; reference household is a single middle-aged male, born in Australia, not financially constrained, same or better standard of living compared with a year ago, working in a high-skilled occupation, with high school as highest level of education and lives in urban NSW Sources: ABS; authors' calculations

Although model outputs are generally similar, some differences are worth highlighting. The effect of education on saving is more pronounced in Model (1) compared with Models (2) and (3), which do not control for the level of current income. This result accords with the intuition that households spend in line with their permanent income, which is correlated with education attainment, and save any deviations between their current and permanent income.

Further, the coefficients on lower-skilled and middle-skilled occupations are positive in Model (1) but negative in Models (2) and (3), which do not control for the level of current income. Although a little puzzling, the difference is likely to reflect the fact that the variables in Models (2) and (3) that are associated with lower levels of current income will also tend to be associated with lower saving, resulting in a negative bias. This issue also applies to other variables correlated with lower current income, for example households containing unemployed people or pensioners.^[17]

Footnote

Note that the income variable used in Model (2) – the deviation of current income from permanent income – will not show low-skilled or middle-skilled workers on average as having a negative deviation of current from permanent income, since skill level is included in the permanent income model. [17]