4.2  The logistic models

The use of logarithms in the core models excludes from analysis those respondents with negative or zero scores for the dependent variable as the logarithm of non-positive numbers is not defined. Logistic models consider the likelihood of an individual having non-positive net wealth and of having no liabilities. These individuals would have been excluded from the core model regressions of net wealth and total liabilities respectively.

Logistic models were chosen rather than probit models. This choice has little to no significance on the resulting fitted models. Logistic models are easier to calculate percentage point effects for and permit a larger variance than probit models.

4.2.1  Non-positive net wealth

Non-positive net wealth arises from having total liabilities equal to or greater than total assets. After adjustments for student loan, 2.5% of the longitudinal population had non-positive net wealth.

This logistic model was built using the same descriptors as core model two with several changes: dwelling tenure and whether the respondent was a student were excluded from the model.[12] It was decided to exclude dwelling tenure as property is typically the largest contributor to net wealth so including it could be misleading. Whether the respondent was a student or not was excluded as adjustments had already been made for the presence of a student loan. The logistic model has the following form:

N_i = ƒ(H,Z'₁,Z'₂) for (i = 1, …, n)

Where:

N_i = 1 if the i^th respondent has negative or zero net wealth
    = 0 if the i^th respondent has net wealth greater than zero

H =The particular health variable being considered

Z'_k = The control variables from the core models

P_i = The probability of N_i = 1

The logistic model has shape:

4.2.2  Zero liabilities

In order to consider total liabilities in the core models, the 28.2% of the longitudinal population who have zero reported liabilities had to be excluded. This makes the regression of total liabilities conditional on having liabilities. In order to provide a fuller picture we use a logistic model for whether an individual has liabilities or not.

The same logistic model as above was used with dwelling tenure and whether the respondent was a student or not being excluded. Dwelling tenure was excluded as the presence of a mortgage would have dominated the model. This logistic model has identical form to the above model specification with one change:

N_i = 1 if the i^th respondent has liabilities
    = 0 if the i^th respondent has zero liabilities

Property and mortgages are the most significant elements of assets and liabilities. According to SoFIE, of those who own property, three-quarters have more than 48% of their assets in property with a value of at least $70,500. Of those with a mortgage, for three-quarters of individuals their mortgage makes up at least 92% of their liabilities, with a value of at least $30,000.

Initial attempts were made to include dwelling tenure in both logistic models. However, as expected, it dominated the model with coefficients at least twice the magnitude of other control variables.