RDP 2022-06: Do Australian Households Borrow to Keep up with the Joneses? 4. Empirical Methodology

To examine the relationship between debt and local income inequality, I estimate the effects of a change in local income inequality on household debt accumulation using a simple reduced-form regression. The reduced-form approach is common in the literature (Coibion et al 2020; Loschiavo 2021) and introduces a number of potential threats to identification. First, the existing literature has shown that household indebtedness is a function of both the supply of and the demand for credit (Cox and Jappelli 1993; Duca and Rosenthal 1993; Browning, Gørtz and Leth-Petersen 2013). The former is driven by household characteristics that the financial institutions consider to determine credit worthiness, while the latter also depends on household preferences, which are generally unobserved. Omitting household characteristics that affect debt accumulation, both observed and unobserved, may bias the estimated effects of local inequality on debt. Second, the supply of and demand for credit is also a function of region-specific macroeconomic and credit conditions that potentially correlate with local income inequality, such as housing prices. As such, omitting these factors could lead to biased estimates. Third, there is a potential reverse causality between debt accumulation and income inequality. Finally, households' mobility choices create a potential selection bias. In this section I discuss in detail the empirical strategies to address these identification concerns.

I first estimate the following baseline regression:

where $\text{Δ}Deb{t}_{ic,t}$ is the debt accumulated between t and t–4 by household i who resides in local area c, measured as a share of household income in t–4. $\text{Δ}Inequalit{y}_{c,t}$ is the change in local income inequality between t and t–4 in local area c, measured in Gini coefficients. ${X^{\prime }}_{ic,t-4}$ is a vector of covariates included to control for time-varying household demographics (e.g. age, education, employment of household head), household structure (e.g. marital status, number of children, number of household members) and household finances (e.g. income, housing wealth, non-housing financial wealth, liquidity). Macro covariates ${Z^{\prime }}_{c,t-4}$ control for time-varying regional measures of housing prices, unemployment rates, income and debt, while I_ict represents regional time trends, where I_ic indicates the SA3 area of household i. All time-varying controls are in lags (t–4) and first differences (between t and t–4). The coefficient of interest is $\beta$, which traces the relationship between a 1 SD increase in Gini coefficient and debt accumulation as a share of income.

I run the regression in first differences to focus on the within-household variation and control for unobserved time-invariant household characteristics such as risk preferences, time preferences and financial literacy, which have been shown to govern household demand for credit and portfolio choices (Browning et al 2013). As such, the approach eliminates concerns regarding omitted time-invariant household-specific factors. It also enables easy interpretation of the heterogeneous effects of local income inequality across different demographic and financial groups.

The macro covariates account for temporal variation in debt accumulation due to changes in macroeconomic and credit conditions over time. I include several such covariates to account for factors that are known to affect debt accumulation, such as the economic cycle and housing prices. I also include a region-specific linear time trend I_ict to help account for other temporal variation, such as changes in the financial regulations and lending standards, as well as borrowing patterns that are specific to the regions. The rich set of observable household characteristics included in ${X^{\prime }}_{ic,t-4}$ control for much of the remaining within-household variation that governs the supply of credit. Taken together, these factors should help to account for other factors that could drive both income inequality and debt accumulation.

Importantly, there are still potential issues around reverse causality. That is, changes in household indebtedness could lead to changes in local income inequality. This would be more concerning if the focus was on wealth or consumption inequality, as both can be affected by household portfolio choices. However, it is less of a concern for income inequality. In particular, income inequality is not dependent on debt accumulation that is wealth generating (housing debt), or debt that services consumption (car debt and credit card debt). And while investment debt may generate dividend income and investment property debt may generate rental income, these sources of income constitute a negligible proportion (0.3 per cent) of personal income measure used by the ABS to construct inequality.^[4]

Still, it is worth considering how such reverse causality could bias the results. If there is a systematic increase in investment debt from the lower end of the distribution, it may, in turn, lower income inequality. As such, there should be a negative feedback from investment debt to inequality. By contrast, if investment debt accumulation is driven by the top of the distribution, it could aggravate income inequality, resulting in a positive relationship between the two. Finally, if the recipients of extra investment income from investment debt are in the middle of the distribution, the change in Gini coefficient will be minimal (Gastwirth 2017). Heterogeneity analysis across the income distribution would shed light on the direction of the bias caused by reverse causality.

As noted before, another econometric issue may arise if households choose to move closer to their reference group, making local inequality endogenous to household debt for households that move out of their initial local region. To eliminate this source of endogeneity, I estimate Equation (1) on the sample of households that do not move out of their initial SA3 region throughout the entire observation period. However, the non-moving households may not be a random sample, which introduces selection bias. I address this concern using a Heckman selection model in the robustness section.

Even after accounting for all these potential biases, it is worth noting that the empirical model does not establish causality as there could still be some unobserved time-varying factors at the local level that I cannot fully control for. As such, the estimates are more suggestive of a relationship, rather than sharply identifying the causal effects of local income inequality on household debt. The non-causal evidence is, nevertheless, useful to understand the mechanisms that potentially drive this relationship.

To better understand the mechanisms and implications behind any relationship between local income inequality and household debt, I perform two extensions. First, I re-run the baseline model for different components of household debt. Second, to look at heterogeneous effect across households I modify the model specification to allow for the interaction between inequality and household characteristics:

where Group_ic,t–4 indicates the demographic or financial group the household belonged to in previous period, which reduces concerns about feedback from household behaviour to their characteristics. I explore heterogeneous effects of local income inequality along several dimensions: income ranking and financial prosperity, life cycle and housing status, and financial constraints and attitude.

Importantly, the heterogeneity in debt accumulation across demographic and financial groups may be driven by the heterogeneous effects of other macro factors, which are loaded onto inequality if not controlled for. For instance, changes in local housing prices are more likely to relax credit constraints for lower income households, and so have a larger effect on their debt accumulation. To isolate the variation due to changes in local income inequality, I control for the interactions between the SA3-level macro covariates ${Z^{\prime }}_{c,t-4}$ and household characteristics.^[5]

Footnotes

See the ABS release ‘Household Income and Wealth, Australia’ for the 2017-18 financial year. [4]

The heterogeneous interactions between individual household-level characteristics are unlikely to confound the heterogeneous effects of SA3-level inequality. [5]